Classification_MNIST_2_pca_git.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Name: Ibrahim Odumas Odufowora <br />\n",
    "Project Name: Classification with MNIST <br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problems Identification:\n",
    "This project involves the implementation of efficient and effective KNN classifiers on MNIST data set. The MNIST data comprises of digital images of several digits ranging from 0 to 9. Each image is 28 x 28 pixels. Thus, the data set has 10 levels of classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are the needed packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window.Plotly) {{require(['plotly'],function(plotly) {window.Plotly=plotly;});}}</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import mode\n",
    "import numpy as np\n",
    "from mnist import MNIST\n",
    "from time import time\n",
    "import pandas as pd\n",
    "import os\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "plt.rcdefaults()\n",
    "from IPython.display import display, HTML\n",
    "from itertools import chain\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from pylab import subplot\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
    "init_notebook_mode(connected=True)\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from plotly.graph_objs import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the dataset, having downloaded it from Yann. The train data set comprises of 60,000 samples and the test data set has 10,000 samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mndata = MNIST(os.getcwd() +'\\\\image')\n",
    "train_image, train_label = mndata.load_training() #train & train_label\n",
    "test_image, test_label = mndata.load_testing() #test & test_label\n",
    "\n",
    "train = np.asarray([np.reshape(x, (784)) for x in train_image]) #change train_image to numpy array #784 means 28 by 28 pixel\n",
    "train_label = np.asarray(train_label)\n",
    "test = np.asarray([np.reshape(x, (784)) for x in test_image]) #change test_image to numpy array\n",
    "test_label = np.asarray(test_label)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The train and test images were reshaped to 784 dimension long, which translate to one feature for each pixel in the image."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualization:\n",
    "Visualizing a random 28 by 28 image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaQAAAGzCAYAAABgn2MWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEQgkAIAR/g8oMXFNBI2kMAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ae1e5ccf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.reshape(train[random.randint(1,1000)], [28,28]), cmap='Greys_r'); plt.title('Visualizing a random sample'); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def knn_error_per_class(train, train_label, test, test_label, k):\n",
    "    st_time = time()\n",
    "    classifier = [[], [], [], [], [], [], [], [], [], []] #10 classes\n",
    "    error_per_class = []\n",
    "    count = []\n",
    "    confusionMatrix = []\n",
    "    for i, val in enumerate(test_label):\n",
    "        diff = (train - test[i])\n",
    "        dist = np.einsum('ij, ij->i', diff, diff)  # quick distance measure\n",
    "        nearest_lbs = train_label[np.argsort(dist)[:k]]\n",
    "        major = mode(nearest_lbs)[0][0]\n",
    "        confusionMatrix.append(major)\n",
    "\n",
    "        for j in range(len(classifier)):\n",
    "            if j == val:\n",
    "                if major == val:\n",
    "                    classifier[j].append(1)\n",
    "                else:\n",
    "                    classifier[j].append(0)\n",
    "                break\n",
    "\n",
    "    for c in range(len(classifier)):\n",
    "        error_per_class.append(1 - np.mean(classifier[c]))\n",
    "        count.append(len(classifier[c]))\n",
    "\n",
    "    return [error_per_class, count, classifier, (time()-st_time), confusionMatrix]\n",
    "\n",
    "def confusionMatrix(actual, predict, isprint=True):\n",
    "    cfm = pd.DataFrame(confusion_matrix(actual, predict))\n",
    "    if isprint == True:\n",
    "        print('Testing Confusion Matrix: Actual vs. Prediction')\n",
    "        display(cfm)\n",
    "    return cfm\n",
    "\n",
    "def error_per_digit(knn_per_err, k):\n",
    "    tab_error = pd.DataFrame(columns=['digit', 'error per digit in %'])\n",
    "    tab_error['digit'] = range(len(knn_per_err[0]))\n",
    "    tab_error['error per digit in %'] = np.round(np.asarray(knn_per_err[0]) * 100, 4)\n",
    "    display(tab_error)\n",
    "    unlist_classes = list(chain.from_iterable(knn_per_err[2]))\n",
    "    overall_error = round(1 - np.mean(unlist_classes), 4)\n",
    "    print('\\nThe overall testing error is {}% for k = {}.'.format(round(overall_error*100, 4), k))\n",
    "\n",
    "def my_knn_loocv(train_all, train_label_all, k_all):\n",
    "    st_time = time()\n",
    "    dt_classifier = pd.DataFrame(index=range(len(train_label_all)), columns=range(len(k_all)))\n",
    "    for j, res in enumerate(train_label_all):\n",
    "        test = train_all[j]\n",
    "        test_label = train_label_all[j]\n",
    "        train = np.delete(train_all, j, 0)\n",
    "        train_label = np.delete(train_label_all, j)\n",
    "\n",
    "        diff = (train - test)\n",
    "        dist = np.einsum('ij, ij->i', diff, diff)  # quick distance measure\n",
    "        for k, k_val in enumerate(k_all):\n",
    "            nearest_lbs = train_label[np.argsort(dist)[:k_val]]\n",
    "            major = mode(nearest_lbs)[0][0]\n",
    "            if major == test_label:\n",
    "                dt_classifier.iloc[j][k] = 1\n",
    "            else:\n",
    "                dt_classifier.iloc[j][k] = 0\n",
    "\n",
    "    dt_error = 1 - dt_classifier.mean(axis=0)\n",
    "    return [dt_error, dt_classifier, (time()-st_time)]\n",
    "\n",
    "def loocv_error_per_k(knn_loocv, k_list):\n",
    "    k_error = np.round(np.asarray(knn_loocv[0]) * 100, 4)\n",
    "    best_k = list(np.argsort(k_error)[:1] + 1).pop()\n",
    "    err_best_k = list(k_error[np.argsort(k_error)[:1]]).pop()\n",
    "    plt.plot(k_list, k_error, '-gD', color='black')\n",
    "    ax = subplot(111)\n",
    "    ax.set_xticks(np.arange(0, 21, 1))\n",
    "    plt.ylabel('% Error')\n",
    "    plt.xlabel('K')\n",
    "    plt.title('Plot of K vs. leave-one-out error')\n",
    "    plt.show()\n",
    "    print('The best value of K is {} with an error of {}%'.format(best_k, err_best_k))\n",
    "    print('\\nK = {} will be used for the testing set:'.format(best_k))\n",
    "    return [best_k, err_best_k]\n",
    "\n",
    "def knn_loocv_method(train, train_label, test, test_label, k_list=range(1, 21)):\n",
    "    knn_loocv = my_knn_loocv(train_all=train, train_label_all=train_label, k_all=k_list)\n",
    "    loocv = loocv_error_per_k(knn_loocv, k_list)\n",
    "    knn_per_err = knn_error_per_class(train=train, train_label=train_label, test=test, test_label=test_label, k=loocv[0])\n",
    "    confusionMatrix(test_label, knn_per_err[4], isprint=True)\n",
    "    error_per_digit(knn_per_err, loocv[0])\n",
    "    return knn_per_err\n",
    "    \n",
    "def my_PCA(jupyter=True, scale_norm=False, data=train): #PCA Basis Function\n",
    "    #There is no need to center and scale because the original data has been centered and scaled\n",
    "    if scale_norm == True:\n",
    "        data = np.asarray(data)\n",
    "        mean = np.mean(data, axis=0)\n",
    "        std = np.std(data, axis=0)\n",
    "        data = (data - mean) / std\n",
    "\n",
    "    covariance_matrix = np.cov(data.T)  # Covariance Matrix of the normalized data\n",
    "    # eigenValues and eigenvectors of the covariance Matrix\n",
    "    # the eigenvectors only define the directions of the new axis\n",
    "    eigenvals, eigenvecs = np.linalg.eig(covariance_matrix)\n",
    "    eigenvals = eigenvals.real\n",
    "    eigenvecs = eigenvecs.real\n",
    "\n",
    "    #computing singular value decomposion\n",
    "    #This was done to check if singular value decomposition is similar results as the eigenvalues and eigenvectors\n",
    "    U, s, V = np.linalg.svd(covariance_matrix, full_matrices=True)\n",
    "\n",
    "    # confirming that the unit length of each of the eigenvector is 1\n",
    "    eigenvecs_lens = []\n",
    "    for i in range(len(eigenvecs)):\n",
    "        eigenvecs_lens.append(np.linalg.norm(eigenvecs[i]))\n",
    "\n",
    "    sum_eigenval = sum(eigenvals)\n",
    "    var_expl = [(i / sum_eigenval) * 100 for i in sorted(eigenvals, reverse=True)] #Variance Explained\n",
    "    cum_var_exp = np.cumsum(var_expl) #Cummulative varinace explained\n",
    "    leng = len(eigenvals) + 1\n",
    "    #bar_data = Bar(x=['PC %s' % i for i in range(1, leng)], y=var_expl, showlegend=False)\n",
    "    scatter_data = Scatter(x=['PC %s' % i for i in range(1, leng)], y=cum_var_exp, name='cumulative explained variance')\n",
    "    #data = Data([bar_data, scatter_data])\n",
    "    data_plt = Data([scatter_data])\n",
    "    layout = Layout(yaxis=YAxis(title='explained variance in percent'), title='Cumulative Explained variance by different principal components 1 - 784')\n",
    "    fig = Figure(data=data_plt, layout=layout)\n",
    "    if jupyter == True:\n",
    "        iplot(fig)\n",
    "    else:\n",
    "        plot(fig)\n",
    "\n",
    "    return [eigenvecs, eigenvals, eigenvecs_lens, U]\n",
    "\n",
    "def pca_transform_results(error, var, comp, best_K, querytim):\n",
    "    tab = pd.DataFrame(columns=['% variance Explain', 'no of components', 'best K used','test error in %', 'query time (ms)'])\n",
    "    tab['% variance Explain'] =  var\n",
    "    tab['no of components'] =  comp\n",
    "    tab['best K used'] =  best_K\n",
    "    tab['test error in %'] =  error\n",
    "    tab['query time (ms)'] =  querytim\n",
    "    display(tab)\n",
    "    \n",
    "    plt.subplots(figsize=(20, 10))\n",
    "    plt.plot(comp, error, label=\"test error rate (%)\") \n",
    "    plt.plot(comp, querytim, label=\"query time (ms)\")\n",
    "    plt.plot(comp, best_K, label=\"best k used\")\n",
    "    plt.xlabel('number of components used')\n",
    "    plt.xticks(comp, comp)\n",
    "    plt.legend()\n",
    "    plt.title('Plot of PCA components used vs. Test Error, Best value of k, and Query Time')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Method - Dimension Reduction (PCA): \n",
    "I implemented a function called my_PCA, it returns the corresponding basis vectors, it also plots cumulative explained variance by the different component. The total components is 784. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reduce data from n-dimension to m-dimension:\n",
    "\n",
    "Transformation using my function (my_PCA) involves the use of the train set to derive basis vectors of 784 components. The steps are outlined below:\n",
    "1. The original images have been centered and scaled, thus there is no need to apply centering and scaling.\n",
    "2. Obtain the covariance matrix of the data\n",
    "\n",
    "    $$\\sum = \\frac{1}{N}\\sum_{i=1}^{n}\\left ( X^{\\left ( i \\right )} \\right )^{T}\\left ( X^{\\left ( i \\right )} \\right )$$\n",
    "    \n",
    "    This will result in a n x n matrix <br>\n",
    "    \n",
    "    \n",
    "3. Derive the eigenvectors and eigenvalues from the covariance matrix \n",
    "4. Confirm that the all the eigenvectors has a unit length of 1\n",
    "5. Plot cumulative variance explained by using sorted the eigenvalues in descending order\n",
    "6. Having gotten the eigenvectors, then transform the original datasets via basis vectors to obtain a reduced dimension depending on the desired explained variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "data": [
        {
         "name": "cumulative explained variance",
         "type": "scatter",
         "x": [
          "PC 1",
          "PC 2",
          "PC 3",
          "PC 4",
          "PC 5",
          "PC 6",
          "PC 7",
          "PC 8",
          "PC 9",
          "PC 10",
          "PC 11",
          "PC 12",
          "PC 13",
          "PC 14",
          "PC 15",
          "PC 16",
          "PC 17",
          "PC 18",
          "PC 19",
          "PC 20",
          "PC 21",
          "PC 22",
          "PC 23",
          "PC 24",
          "PC 25",
          "PC 26",
          "PC 27",
          "PC 28",
          "PC 29",
          "PC 30",
          "PC 31",
          "PC 32",
          "PC 33",
          "PC 34",
          "PC 35",
          "PC 36",
          "PC 37",
          "PC 38",
          "PC 39",
          "PC 40",
          "PC 41",
          "PC 42",
          "PC 43",
          "PC 44",
          "PC 45",
          "PC 46",
          "PC 47",
          "PC 48",
          "PC 49",
          "PC 50",
          "PC 51",
          "PC 52",
          "PC 53",
          "PC 54",
          "PC 55",
          "PC 56",
          "PC 57",
          "PC 58",
          "PC 59",
          "PC 60",
          "PC 61",
          "PC 62",
          "PC 63",
          "PC 64",
          "PC 65",
          "PC 66",
          "PC 67",
          "PC 68",
          "PC 69",
          "PC 70",
          "PC 71",
          "PC 72",
          "PC 73",
          "PC 74",
          "PC 75",
          "PC 76",
          "PC 77",
          "PC 78",
          "PC 79",
          "PC 80",
          "PC 81",
          "PC 82",
          "PC 83",
          "PC 84",
          "PC 85",
          "PC 86",
          "PC 87",
          "PC 88",
          "PC 89",
          "PC 90",
          "PC 91",
          "PC 92",
          "PC 93",
          "PC 94",
          "PC 95",
          "PC 96",
          "PC 97",
          "PC 98",
          "PC 99",
          "PC 100",
          "PC 101",
          "PC 102",
          "PC 103",
          "PC 104",
          "PC 105",
          "PC 106",
          "PC 107",
          "PC 108",
          "PC 109",
          "PC 110",
          "PC 111",
          "PC 112",
          "PC 113",
          "PC 114",
          "PC 115",
          "PC 116",
          "PC 117",
          "PC 118",
          "PC 119",
          "PC 120",
          "PC 121",
          "PC 122",
          "PC 123",
          "PC 124",
          "PC 125",
          "PC 126",
          "PC 127",
          "PC 128",
          "PC 129",
          "PC 130",
          "PC 131",
          "PC 132",
          "PC 133",
          "PC 134",
          "PC 135",
          "PC 136",
          "PC 137",
          "PC 138",
          "PC 139",
          "PC 140",
          "PC 141",
          "PC 142",
          "PC 143",
          "PC 144",
          "PC 145",
          "PC 146",
          "PC 147",
          "PC 148",
          "PC 149",
          "PC 150",
          "PC 151",
          "PC 152",
          "PC 153",
          "PC 154",
          "PC 155",
          "PC 156",
          "PC 157",
          "PC 158",
          "PC 159",
          "PC 160",
          "PC 161",
          "PC 162",
          "PC 163",
          "PC 164",
          "PC 165",
          "PC 166",
          "PC 167",
          "PC 168",
          "PC 169",
          "PC 170",
          "PC 171",
          "PC 172",
          "PC 173",
          "PC 174",
          "PC 175",
          "PC 176",
          "PC 177",
          "PC 178",
          "PC 179",
          "PC 180",
          "PC 181",
          "PC 182",
          "PC 183",
          "PC 184",
          "PC 185",
          "PC 186",
          "PC 187",
          "PC 188",
          "PC 189",
          "PC 190",
          "PC 191",
          "PC 192",
          "PC 193",
          "PC 194",
          "PC 195",
          "PC 196",
          "PC 197",
          "PC 198",
          "PC 199",
          "PC 200",
          "PC 201",
          "PC 202",
          "PC 203",
          "PC 204",
          "PC 205",
          "PC 206",
          "PC 207",
          "PC 208",
          "PC 209",
          "PC 210",
          "PC 211",
          "PC 212",
          "PC 213",
          "PC 214",
          "PC 215",
          "PC 216",
          "PC 217",
          "PC 218",
          "PC 219",
          "PC 220",
          "PC 221",
          "PC 222",
          "PC 223",
          "PC 224",
          "PC 225",
          "PC 226",
          "PC 227",
          "PC 228",
          "PC 229",
          "PC 230",
          "PC 231",
          "PC 232",
          "PC 233",
          "PC 234",
          "PC 235",
          "PC 236",
          "PC 237",
          "PC 238",
          "PC 239",
          "PC 240",
          "PC 241",
          "PC 242",
          "PC 243",
          "PC 244",
          "PC 245",
          "PC 246",
          "PC 247",
          "PC 248",
          "PC 249",
          "PC 250",
          "PC 251",
          "PC 252",
          "PC 253",
          "PC 254",
          "PC 255",
          "PC 256",
          "PC 257",
          "PC 258",
          "PC 259",
          "PC 260",
          "PC 261",
          "PC 262",
          "PC 263",
          "PC 264",
          "PC 265",
          "PC 266",
          "PC 267",
          "PC 268",
          "PC 269",
          "PC 270",
          "PC 271",
          "PC 272",
          "PC 273",
          "PC 274",
          "PC 275",
          "PC 276",
          "PC 277",
          "PC 278",
          "PC 279",
          "PC 280",
          "PC 281",
          "PC 282",
          "PC 283",
          "PC 284",
          "PC 285",
          "PC 286",
          "PC 287",
          "PC 288",
          "PC 289",
          "PC 290",
          "PC 291",
          "PC 292",
          "PC 293",
          "PC 294",
          "PC 295",
          "PC 296",
          "PC 297",
          "PC 298",
          "PC 299",
          "PC 300",
          "PC 301",
          "PC 302",
          "PC 303",
          "PC 304",
          "PC 305",
          "PC 306",
          "PC 307",
          "PC 308",
          "PC 309",
          "PC 310",
          "PC 311",
          "PC 312",
          "PC 313",
          "PC 314",
          "PC 315",
          "PC 316",
          "PC 317",
          "PC 318",
          "PC 319",
          "PC 320",
          "PC 321",
          "PC 322",
          "PC 323",
          "PC 324",
          "PC 325",
          "PC 326",
          "PC 327",
          "PC 328",
          "PC 329",
          "PC 330",
          "PC 331",
          "PC 332",
          "PC 333",
          "PC 334",
          "PC 335",
          "PC 336",
          "PC 337",
          "PC 338",
          "PC 339",
          "PC 340",
          "PC 341",
          "PC 342",
          "PC 343",
          "PC 344",
          "PC 345",
          "PC 346",
          "PC 347",
          "PC 348",
          "PC 349",
          "PC 350",
          "PC 351",
          "PC 352",
          "PC 353",
          "PC 354",
          "PC 355",
          "PC 356",
          "PC 357",
          "PC 358",
          "PC 359",
          "PC 360",
          "PC 361",
          "PC 362",
          "PC 363",
          "PC 364",
          "PC 365",
          "PC 366",
          "PC 367",
          "PC 368",
          "PC 369",
          "PC 370",
          "PC 371",
          "PC 372",
          "PC 373",
          "PC 374",
          "PC 375",
          "PC 376",
          "PC 377",
          "PC 378",
          "PC 379",
          "PC 380",
          "PC 381",
          "PC 382",
          "PC 383",
          "PC 384",
          "PC 385",
          "PC 386",
          "PC 387",
          "PC 388",
          "PC 389",
          "PC 390",
          "PC 391",
          "PC 392",
          "PC 393",
          "PC 394",
          "PC 395",
          "PC 396",
          "PC 397",
          "PC 398",
          "PC 399",
          "PC 400",
          "PC 401",
          "PC 402",
          "PC 403",
          "PC 404",
          "PC 405",
          "PC 406",
          "PC 407",
          "PC 408",
          "PC 409",
          "PC 410",
          "PC 411",
          "PC 412",
          "PC 413",
          "PC 414",
          "PC 415",
          "PC 416",
          "PC 417",
          "PC 418",
          "PC 419",
          "PC 420",
          "PC 421",
          "PC 422",
          "PC 423",
          "PC 424",
          "PC 425",
          "PC 426",
          "PC 427",
          "PC 428",
          "PC 429",
          "PC 430",
          "PC 431",
          "PC 432",
          "PC 433",
          "PC 434",
          "PC 435",
          "PC 436",
          "PC 437",
          "PC 438",
          "PC 439",
          "PC 440",
          "PC 441",
          "PC 442",
          "PC 443",
          "PC 444",
          "PC 445",
          "PC 446",
          "PC 447",
          "PC 448",
          "PC 449",
          "PC 450",
          "PC 451",
          "PC 452",
          "PC 453",
          "PC 454",
          "PC 455",
          "PC 456",
          "PC 457",
          "PC 458",
          "PC 459",
          "PC 460",
          "PC 461",
          "PC 462",
          "PC 463",
          "PC 464",
          "PC 465",
          "PC 466",
          "PC 467",
          "PC 468",
          "PC 469",
          "PC 470",
          "PC 471",
          "PC 472",
          "PC 473",
          "PC 474",
          "PC 475",
          "PC 476",
          "PC 477",
          "PC 478",
          "PC 479",
          "PC 480",
          "PC 481",
          "PC 482",
          "PC 483",
          "PC 484",
          "PC 485",
          "PC 486",
          "PC 487",
          "PC 488",
          "PC 489",
          "PC 490",
          "PC 491",
          "PC 492",
          "PC 493",
          "PC 494",
          "PC 495",
          "PC 496",
          "PC 497",
          "PC 498",
          "PC 499",
          "PC 500",
          "PC 501",
          "PC 502",
          "PC 503",
          "PC 504",
          "PC 505",
          "PC 506",
          "PC 507",
          "PC 508",
          "PC 509",
          "PC 510",
          "PC 511",
          "PC 512",
          "PC 513",
          "PC 514",
          "PC 515",
          "PC 516",
          "PC 517",
          "PC 518",
          "PC 519",
          "PC 520",
          "PC 521",
          "PC 522",
          "PC 523",
          "PC 524",
          "PC 525",
          "PC 526",
          "PC 527",
          "PC 528",
          "PC 529",
          "PC 530",
          "PC 531",
          "PC 532",
          "PC 533",
          "PC 534",
          "PC 535",
          "PC 536",
          "PC 537",
          "PC 538",
          "PC 539",
          "PC 540",
          "PC 541",
          "PC 542",
          "PC 543",
          "PC 544",
          "PC 545",
          "PC 546",
          "PC 547",
          "PC 548",
          "PC 549",
          "PC 550",
          "PC 551",
          "PC 552",
          "PC 553",
          "PC 554",
          "PC 555",
          "PC 556",
          "PC 557",
          "PC 558",
          "PC 559",
          "PC 560",
          "PC 561",
          "PC 562",
          "PC 563",
          "PC 564",
          "PC 565",
          "PC 566",
          "PC 567",
          "PC 568",
          "PC 569",
          "PC 570",
          "PC 571",
          "PC 572",
          "PC 573",
          "PC 574",
          "PC 575",
          "PC 576",
          "PC 577",
          "PC 578",
          "PC 579",
          "PC 580",
          "PC 581",
          "PC 582",
          "PC 583",
          "PC 584",
          "PC 585",
          "PC 586",
          "PC 587",
          "PC 588",
          "PC 589",
          "PC 590",
          "PC 591",
          "PC 592",
          "PC 593",
          "PC 594",
          "PC 595",
          "PC 596",
          "PC 597",
          "PC 598",
          "PC 599",
          "PC 600",
          "PC 601",
          "PC 602",
          "PC 603",
          "PC 604",
          "PC 605",
          "PC 606",
          "PC 607",
          "PC 608",
          "PC 609",
          "PC 610",
          "PC 611",
          "PC 612",
          "PC 613",
          "PC 614",
          "PC 615",
          "PC 616",
          "PC 617",
          "PC 618",
          "PC 619",
          "PC 620",
          "PC 621",
          "PC 622",
          "PC 623",
          "PC 624",
          "PC 625",
          "PC 626",
          "PC 627",
          "PC 628",
          "PC 629",
          "PC 630",
          "PC 631",
          "PC 632",
          "PC 633",
          "PC 634",
          "PC 635",
          "PC 636",
          "PC 637",
          "PC 638",
          "PC 639",
          "PC 640",
          "PC 641",
          "PC 642",
          "PC 643",
          "PC 644",
          "PC 645",
          "PC 646",
          "PC 647",
          "PC 648",
          "PC 649",
          "PC 650",
          "PC 651",
          "PC 652",
          "PC 653",
          "PC 654",
          "PC 655",
          "PC 656",
          "PC 657",
          "PC 658",
          "PC 659",
          "PC 660",
          "PC 661",
          "PC 662",
          "PC 663",
          "PC 664",
          "PC 665",
          "PC 666",
          "PC 667",
          "PC 668",
          "PC 669",
          "PC 670",
          "PC 671",
          "PC 672",
          "PC 673",
          "PC 674",
          "PC 675",
          "PC 676",
          "PC 677",
          "PC 678",
          "PC 679",
          "PC 680",
          "PC 681",
          "PC 682",
          "PC 683",
          "PC 684",
          "PC 685",
          "PC 686",
          "PC 687",
          "PC 688",
          "PC 689",
          "PC 690",
          "PC 691",
          "PC 692",
          "PC 693",
          "PC 694",
          "PC 695",
          "PC 696",
          "PC 697",
          "PC 698",
          "PC 699",
          "PC 700",
          "PC 701",
          "PC 702",
          "PC 703",
          "PC 704",
          "PC 705",
          "PC 706",
          "PC 707",
          "PC 708",
          "PC 709",
          "PC 710",
          "PC 711",
          "PC 712",
          "PC 713",
          "PC 714",
          "PC 715",
          "PC 716",
          "PC 717",
          "PC 718",
          "PC 719",
          "PC 720",
          "PC 721",
          "PC 722",
          "PC 723",
          "PC 724",
          "PC 725",
          "PC 726",
          "PC 727",
          "PC 728",
          "PC 729",
          "PC 730",
          "PC 731",
          "PC 732",
          "PC 733",
          "PC 734",
          "PC 735",
          "PC 736",
          "PC 737",
          "PC 738",
          "PC 739",
          "PC 740",
          "PC 741",
          "PC 742",
          "PC 743",
          "PC 744",
          "PC 745",
          "PC 746",
          "PC 747",
          "PC 748",
          "PC 749",
          "PC 750",
          "PC 751",
          "PC 752",
          "PC 753",
          "PC 754",
          "PC 755",
          "PC 756",
          "PC 757",
          "PC 758",
          "PC 759",
          "PC 760",
          "PC 761",
          "PC 762",
          "PC 763",
          "PC 764",
          "PC 765",
          "PC 766",
          "PC 767",
          "PC 768",
          "PC 769",
          "PC 770",
          "PC 771",
          "PC 772",
          "PC 773",
          "PC 774",
          "PC 775",
          "PC 776",
          "PC 777",
          "PC 778",
          "PC 779",
          "PC 780",
          "PC 781",
          "PC 782",
          "PC 783",
          "PC 784"
         ],
         "y": [
          9.704664359713888,
          16.800588418808374,
          22.969677181176486,
          28.359096667729887,
          33.22789369120473,
          37.54012500649849,
          40.81205496032024,
          43.69595040652464,
          46.45797980529533,
          48.814980354934,
          50.924169970000996,
          52.94716105178833,
          54.66297925131915,
          56.35509068339043,
          57.93373196389916,
          59.41668457712042,
          60.741245528024585,
          62.01814289580257,
          63.20540583539684,
          64.3580895367477,
          65.42425574383309,
          66.43096911580751,
          67.38454244265357,
          68.29708618833114,
          69.18049087999616,
          70.01981002072027,
          70.83238883018939,
          71.61875491432265,
          72.363488016634,
          73.05434714429178,
          73.71244091690382,
          74.36058878685573,
          74.96320381701013,
          75.54978600486835,
          76.11980747920471,
          76.6634352499748,
          77.16922166634606,
          77.65708026995006,
          78.13850961160838,
          78.61077593790242,
          79.0675228587842,
          79.51235887052816,
          79.93086019967394,
          80.32907553836802,
          80.71405014571822,
          81.0891535326744,
          81.45116238434063,
          81.80275366116976,
          82.14281186628807,
          82.4646863333473,
          82.78370338399554,
          83.09650832314037,
          83.39249099099732,
          83.68144559061012,
          83.96557598870221,
          84.2370118001449,
          84.50653325355515,
          84.7650057990682,
          85.01877639284683,
          85.26355735244742,
          85.50406348495544,
          85.74332638642011,
          85.97373487565606,
          86.19526700710816,
          86.40898782296465,
          86.6162130625417,
          86.81925573384589,
          87.01603834944159,
          87.20889094366244,
          87.39752342224655,
          87.58450048792722,
          87.76558347070038,
          87.94314557222891,
          88.1180436452053,
          88.28380186481431,
          88.44769578688899,
          88.609157900804,
          88.7642743242466,
          88.9118872982051,
          89.05506336381052,
          89.1971575914646,
          89.33831078095065,
          89.47848519542232,
          89.6142215383099,
          89.7480686807244,
          89.88046501416069,
          90.01062226425093,
          90.13649535379415,
          90.25932351354234,
          90.3809079992643,
          90.49794246115557,
          90.61281605166636,
          90.72606023472898,
          90.83694587461494,
          90.94594768362207,
          91.05287091767234,
          91.15706689215087,
          91.26107370768165,
          91.3623299877357,
          91.46285724395082,
          91.56125897319798,
          91.65622759572733,
          91.75036168104954,
          91.84197831994379,
          91.93276338782567,
          92.02245061262595,
          92.10898974229245,
          92.19450695441307,
          92.27906894854779,
          92.36131851143068,
          92.44047693682379,
          92.51907080626215,
          92.59753147671401,
          92.6744146320085,
          92.75081618146474,
          92.82612501748596,
          92.89980331016854,
          92.97251650295175,
          93.04448166732922,
          93.11516329574509,
          93.18470573980028,
          93.25392185132726,
          93.32225218656697,
          93.38965824171136,
          93.45634592305616,
          93.52087249681655,
          93.58443191165225,
          93.64759653961292,
          93.70988990800225,
          93.77041893236165,
          93.83077779918644,
          93.89022589636376,
          93.94905667009768,
          94.00770867581848,
          94.06584276497696,
          94.12352589816308,
          94.18006280944857,
          94.23553925721104,
          94.28905628923621,
          94.34164882596906,
          94.39415814725682,
          94.44518384059977,
          94.49548091969676,
          94.54558870591632,
          94.59545998867483,
          94.64456697810171,
          94.69312073606845,
          94.7414053695528,
          94.78880675165485,
          94.83564188145836,
          94.8823017771185,
          94.92863456560555,
          94.97456393815953,
          95.01960192613038,
          95.06448266584884,
          95.10875365848221,
          95.1524210920029,
          95.19516594258756,
          95.2376638646023,
          95.27986510464166,
          95.32141645808909,
          95.36238016414215,
          95.40246254171977,
          95.44225077003524,
          95.48165884374002,
          95.52070820060929,
          95.55929345873606,
          95.59727111372246,
          95.6351610300652,
          95.6725549644378,
          95.70949642118724,
          95.74601149002234,
          95.7823928169557,
          95.81838027820083,
          95.85384450097774,
          95.88913429787792,
          95.92386314266986,
          95.958458866936,
          95.9926035729305,
          96.02636814271713,
          96.06007754332006,
          96.09310024599397,
          96.12593573177561,
          96.15852646655009,
          96.19082091902293,
          96.22294783216316,
          96.25467776110929,
          96.28629526090513,
          96.31738951550199,
          96.3483432032713,
          96.37893983966687,
          96.40926731605876,
          96.4395083461272,
          96.46966521915725,
          96.49933593991602,
          96.52891059681778,
          96.5582577701243,
          96.58752502085426,
          96.61630024873087,
          96.64473477010526,
          96.67293139572227,
          96.70083842135139,
          96.72841187764327,
          96.75565933862424,
          96.78260286499933,
          96.80937359913341,
          96.83588560807378,
          96.86231832194912,
          96.88850661125947,
          96.91445170279411,
          96.94030739459915,
          96.96599967491895,
          96.99147337348354,
          97.01675457229655,
          97.04198355533465,
          97.06693984795648,
          97.09179151145435,
          97.11639900641067,
          97.14079449915968,
          97.16498080833772,
          97.18907762304275,
          97.21312201556192,
          97.23694899720432,
          97.26063433623916,
          97.28389214513392,
          97.30702303782503,
          97.33003584431381,
          97.3528445190116,
          97.37560285319056,
          97.39788047474185,
          97.42006677592103,
          97.44211101044112,
          97.46389766826618,
          97.48556331265948,
          97.50707970601441,
          97.52849919313361,
          97.54978470622649,
          97.57082195471423,
          97.59179745733822,
          97.61249360244149,
          97.63296599835985,
          97.65339312436367,
          97.67352454952413,
          97.69362303195022,
          97.71352268756863,
          97.73328575183879,
          97.75286849651184,
          97.77224132038299,
          97.79152716045884,
          97.81070442612378,
          97.82985861876344,
          97.8487663897674,
          97.86756764657231,
          97.88620687584762,
          97.90479162740934,
          97.92325343247605,
          97.94162301660751,
          97.95993763468124,
          97.97812569656784,
          97.99611232981839,
          98.01386790490533,
          98.03153677835752,
          98.04913299272316,
          98.06652127966461,
          98.08386413884476,
          98.10112867569688,
          98.11826723926585,
          98.13527088639066,
          98.15220093780077,
          98.16900148464256,
          98.1856936598304,
          98.20233888912114,
          98.21875945073496,
          98.2351076180398,
          98.25137342346866,
          98.26756247311394,
          98.28365160015417,
          98.29963598453558,
          98.31551927144977,
          98.33125445147743,
          98.34692822514565,
          98.36241793866914,
          98.37779883813401,
          98.3931056320335,
          98.40830951330936,
          98.42331057972957,
          98.43827707287092,
          98.45309999632694,
          98.46786738944382,
          98.48248012761206,
          98.49694536427764,
          98.51126874492456,
          98.52554104312738,
          98.53974799100855,
          98.5539228907991,
          98.56797210862995,
          98.58179587183659,
          98.59559309619054,
          98.60927722267263,
          98.62287476125923,
          98.6364542831316,
          98.6499052009417,
          98.66326692299519,
          98.67650120339057,
          98.68957138428111,
          98.70259033882554,
          98.71550661762952,
          98.72831778065016,
          98.74106934286625,
          98.7537911285177,
          98.76642499733317,
          98.77901100478523,
          98.79148407802805,
          98.80384030880471,
          98.8161024831791,
          98.82825920680233,
          98.84036191384399,
          98.85235865983353,
          98.86430087515521,
          98.8761957524363,
          98.88798296634795,
          98.8996889631474,
          98.91133845459055,
          98.92294835873409,
          98.93440141415735,
          98.94582311052436,
          98.95706376543781,
          98.96819129900472,
          98.97924530777586,
          98.99028838329114,
          99.00129426354096,
          99.01219174685416,
          99.02302405358522,
          99.03378362351845,
          99.04448406057863,
          99.05510455700885,
          99.06569745700877,
          99.0762024392913,
          99.08654449487925,
          99.09676951807991,
          99.10697410272942,
          99.11705867923197,
          99.12708514991705,
          99.13704492597088,
          99.14698221932625,
          99.15679471658491,
          99.16655423069946,
          99.17623734991669,
          99.18578979172918,
          99.19524427549271,
          99.20462409754326,
          99.2139963715142,
          99.22324567701148,
          99.23240442188109,
          99.24154409868737,
          99.25061151743894,
          99.25961903136107,
          99.26855607898422,
          99.27747167501,
          99.2862978140153,
          99.29503060553213,
          99.30366156491633,
          99.31221910421482,
          99.32073487930793,
          99.32919508634231,
          99.33752636832634,
          99.34582416549006,
          99.35407403566548,
          99.36226518707612,
          99.37037422402322,
          99.37846453894105,
          99.38642540276417,
          99.39437223530047,
          99.40223484778369,
          99.41004096143021,
          99.41778348366172,
          99.42544250839406,
          99.43302290004043,
          99.44048386442144,
          99.44786844066273,
          99.45522535320862,
          99.46250691479477,
          99.46977831631683,
          99.47698498748377,
          99.48412662777496,
          99.4912072063956,
          99.49817237222884,
          99.50509687475785,
          99.51192683687577,
          99.51872067621827,
          99.52542653576259,
          99.53204998108396,
          99.53857424362636,
          99.5449944929675,
          99.55136553249754,
          99.55771089095732,
          99.56391416694095,
          99.57004282583387,
          99.57607472825255,
          99.58206755674023,
          99.58800436101775,
          99.59387735147548,
          99.59973941997235,
          99.60547804147458,
          99.61115058121506,
          99.61678796273145,
          99.62234961180243,
          99.62783974069511,
          99.63331362227437,
          99.63876092245374,
          99.64409393756125,
          99.64936949742032,
          99.65462426624693,
          99.65984408998251,
          99.66502929828424,
          99.67013078699999,
          99.67516889093866,
          99.6801444336056,
          99.68505117208038,
          99.68992125447619,
          99.6947154714379,
          99.69943629449239,
          99.70410236386732,
          99.7087466252953,
          99.71330678456538,
          99.71779772709093,
          99.72216907485961,
          99.72646172837092,
          99.73072262870046,
          99.73496119003639,
          99.73917861382239,
          99.74335708729018,
          99.74749579081296,
          99.75158040897468,
          99.75560909361606,
          99.7594679678901,
          99.76329316761857,
          99.7671073570228,
          99.77089574077833,
          99.77462812250742,
          99.77833554702634,
          99.78199456418305,
          99.78557105235308,
          99.78910684765111,
          99.79263215799915,
          99.79611915776127,
          99.7995742139968,
          99.80301257108003,
          99.80635282704904,
          99.80965274502034,
          99.81287259286879,
          99.81606652815412,
          99.81923060914565,
          99.82233191500174,
          99.82537283809616,
          99.8283884405316,
          99.83137906273954,
          99.83430034765958,
          99.83718699436793,
          99.84003883947435,
          99.8428453465662,
          99.845636086627,
          99.84838781876273,
          99.85108235152704,
          99.85365961582318,
          99.8561888221768,
          99.8587051192801,
          99.86118794525038,
          99.86365670159562,
          99.86609234796089,
          99.86852376026137,
          99.87094866196631,
          99.8733212435031,
          99.87565637769599,
          99.87797808590778,
          99.88022992645604,
          99.88246644879239,
          99.88467829362835,
          99.88682153218777,
          99.88895107766622,
          99.89105781483626,
          99.89314344136588,
          99.89518115229056,
          99.89719012609692,
          99.89917657540687,
          99.90113902802977,
          99.90309049583145,
          99.90498645833087,
          99.90683140664098,
          99.90865006745919,
          99.9104603164009,
          99.91225604952527,
          99.91401489173124,
          99.91575588715611,
          99.91739172316846,
          99.91900903270053,
          99.92061986969284,
          99.92221026361482,
          99.92376417411762,
          99.9252847684116,
          99.92680147239211,
          99.92829942382481,
          99.92977527092782,
          99.93123309939281,
          99.93266856659626,
          99.9340862743334,
          99.93548248874853,
          99.9368614607783,
          99.93822891801015,
          99.93956223147319,
          99.94087262586498,
          99.94212749902941,
          99.94336563446146,
          99.9445841626974,
          99.94578431723785,
          99.94697557294953,
          99.94815323466055,
          99.94932630909952,
          99.95046419024823,
          99.95159587507236,
          99.95272051132434,
          99.9538207722528,
          99.95491447502536,
          99.95597148232595,
          99.95702532274315,
          99.95804852577088,
          99.95905071748506,
          99.96000820396293,
          99.96094545225084,
          99.96187148679658,
          99.9627937123409,
          99.96368087774256,
          99.96456185765292,
          99.96542108696596,
          99.9662371055002,
          99.96703409677355,
          99.96782081590965,
          99.96859420974806,
          99.96935859856889,
          99.97011635192477,
          99.97086954640028,
          99.97160640737553,
          99.97233332825525,
          99.97304819462157,
          99.97374435710746,
          99.9744324688394,
          99.97510400514399,
          99.97576958674011,
          99.97642338791242,
          99.97707039930177,
          99.97768438963936,
          99.97827712862774,
          99.97884985219275,
          99.97941757658268,
          99.97997307466991,
          99.98050801264141,
          99.9810350856299,
          99.9815533409017,
          99.9820572632686,
          99.9825568166921,
          99.98305008580677,
          99.98354017344215,
          99.98402123774925,
          99.98449083922857,
          99.9849531680658,
          99.98540862663086,
          99.98582845509361,
          99.98624694491848,
          99.98664821779121,
          99.98704837334988,
          99.98744288666295,
          99.98782286207143,
          99.98820094755285,
          99.98853216533888,
          99.98885595302845,
          99.98917721179977,
          99.98949473108264,
          99.98980668902652,
          99.99011490539446,
          99.9904174872144,
          99.99071870138432,
          99.99101577171857,
          99.99131136509538,
          99.99160382347857,
          99.99188420044094,
          99.99214704598705,
          99.99240203957916,
          99.99263820995785,
          99.99286975682435,
          99.99309605317818,
          99.99332052794396,
          99.99354129707251,
          99.9937564125079,
          99.99397107635086,
          99.99418128030302,
          99.99438545738646,
          99.99457337227729,
          99.99475987854855,
          99.99494509838878,
          99.99512954430163,
          99.99530958133451,
          99.9954850144011,
          99.99564685808012,
          99.99580739879097,
          99.99595774604616,
          99.99610385182422,
          99.99624518208316,
          99.99638401694983,
          99.99651583737958,
          99.99664616131747,
          99.99677462592786,
          99.99689930981614,
          99.99701123014066,
          99.99711907075026,
          99.99722386568598,
          99.99732802394746,
          99.99743159875683,
          99.99752972118775,
          99.997626361699,
          99.99771981096998,
          99.99781138552571,
          99.9979023640495,
          99.99799226994921,
          99.99807980863777,
          99.99816312321674,
          99.99824073634873,
          99.99831523285076,
          99.99838741685141,
          99.99845408023916,
          99.9985200532257,
          99.99858374392095,
          99.99864629998264,
          99.99870883776961,
          99.99876793034491,
          99.99882621895405,
          99.99888290727041,
          99.99893900380516,
          99.99899182532609,
          99.99904405010982,
          99.99909179824387,
          99.9991389647981,
          99.99918557842855,
          99.99922880596887,
          99.99927084965675,
          99.99931149706964,
          99.99934988584135,
          99.99938609884298,
          99.99942176503508,
          99.99945299669011,
          99.99948267976976,
          99.99951052127747,
          99.99953778935289,
          99.99956353784931,
          99.99958909280299,
          99.99961322161217,
          99.99963679218712,
          99.99965978627482,
          99.99968232149733,
          99.99970382104661,
          99.99972407466633,
          99.99974421866109,
          99.99976383548865,
          99.99978150952388,
          99.99979863239395,
          99.9998137317399,
          99.99982870356861,
          99.99984236369187,
          99.99985589415135,
          99.99986869953518,
          99.99987940450735,
          99.99988885347132,
          99.99989763738984,
          99.99990596389475,
          99.99991413199677,
          99.99992098087226,
          99.99992770456,
          99.99993412561723,
          99.99994008450456,
          99.99994562476354,
          99.99995028594378,
          99.9999548794822,
          99.99995894470878,
          99.99996288054915,
          99.99996648510545,
          99.9999700544871,
          99.99997329470388,
          99.99997638231692,
          99.99997938714769,
          99.99998227786394,
          99.99998468036948,
          99.99998656503193,
          99.99998833761123,
          99.99999000060134,
          99.99999162107582,
          99.99999273609028,
          99.99999376677113,
          99.99999477661306,
          99.99999564108428,
          99.99999643688462,
          99.9999971285218,
          99.99999781704565,
          99.99999836026268,
          99.99999885684886,
          99.99999922667102,
          99.99999952870562,
          99.9999997227134,
          99.99999980945177,
          99.99999988027068,
          99.99999994949681,
          99.99999997484746,
          99.99999999846939,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999,
          99.99999999999999
         ]
        }
       ],
       "layout": {
        "title": "Cumulative Explained variance by different principal components 1 - 784",
        "yaxis": {
         "title": "explained variance in percent"
        }
       }
      },
      "text/html": [
       "<div id=\"67d6e4e6-5ea2-48b8-b7a8-c1a58d6b9a41\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"67d6e4e6-5ea2-48b8-b7a8-c1a58d6b9a41\", [{\"type\": \"scatter\", \"x\": [\"PC 1\", \"PC 2\", \"PC 3\", \"PC 4\", \"PC 5\", \"PC 6\", \"PC 7\", \"PC 8\", \"PC 9\", \"PC 10\", \"PC 11\", \"PC 12\", \"PC 13\", \"PC 14\", \"PC 15\", \"PC 16\", \"PC 17\", \"PC 18\", \"PC 19\", \"PC 20\", \"PC 21\", \"PC 22\", \"PC 23\", \"PC 24\", \"PC 25\", \"PC 26\", \"PC 27\", \"PC 28\", \"PC 29\", \"PC 30\", \"PC 31\", \"PC 32\", \"PC 33\", \"PC 34\", \"PC 35\", \"PC 36\", \"PC 37\", \"PC 38\", \"PC 39\", \"PC 40\", \"PC 41\", \"PC 42\", \"PC 43\", \"PC 44\", \"PC 45\", \"PC 46\", \"PC 47\", \"PC 48\", \"PC 49\", \"PC 50\", \"PC 51\", \"PC 52\", \"PC 53\", \"PC 54\", \"PC 55\", \"PC 56\", \"PC 57\", \"PC 58\", \"PC 59\", \"PC 60\", \"PC 61\", \"PC 62\", \"PC 63\", \"PC 64\", \"PC 65\", \"PC 66\", \"PC 67\", \"PC 68\", \"PC 69\", \"PC 70\", \"PC 71\", \"PC 72\", \"PC 73\", \"PC 74\", \"PC 75\", \"PC 76\", \"PC 77\", \"PC 78\", \"PC 79\", \"PC 80\", \"PC 81\", \"PC 82\", \"PC 83\", \"PC 84\", \"PC 85\", \"PC 86\", \"PC 87\", \"PC 88\", \"PC 89\", \"PC 90\", \"PC 91\", \"PC 92\", \"PC 93\", \"PC 94\", \"PC 95\", \"PC 96\", \"PC 97\", \"PC 98\", \"PC 99\", \"PC 100\", \"PC 101\", \"PC 102\", \"PC 103\", \"PC 104\", \"PC 105\", \"PC 106\", \"PC 107\", \"PC 108\", \"PC 109\", \"PC 110\", \"PC 111\", \"PC 112\", \"PC 113\", \"PC 114\", \"PC 115\", \"PC 116\", \"PC 117\", \"PC 118\", \"PC 119\", \"PC 120\", \"PC 121\", \"PC 122\", \"PC 123\", \"PC 124\", \"PC 125\", \"PC 126\", \"PC 127\", \"PC 128\", \"PC 129\", \"PC 130\", \"PC 131\", \"PC 132\", \"PC 133\", \"PC 134\", \"PC 135\", \"PC 136\", \"PC 137\", \"PC 138\", \"PC 139\", \"PC 140\", \"PC 141\", \"PC 142\", \"PC 143\", \"PC 144\", \"PC 145\", \"PC 146\", \"PC 147\", \"PC 148\", \"PC 149\", \"PC 150\", \"PC 151\", \"PC 152\", \"PC 153\", \"PC 154\", \"PC 155\", \"PC 156\", \"PC 157\", \"PC 158\", \"PC 159\", \"PC 160\", \"PC 161\", \"PC 162\", \"PC 163\", \"PC 164\", \"PC 165\", \"PC 166\", \"PC 167\", \"PC 168\", \"PC 169\", \"PC 170\", \"PC 171\", \"PC 172\", \"PC 173\", \"PC 174\", \"PC 175\", \"PC 176\", \"PC 177\", \"PC 178\", \"PC 179\", \"PC 180\", \"PC 181\", \"PC 182\", \"PC 183\", \"PC 184\", \"PC 185\", \"PC 186\", \"PC 187\", \"PC 188\", \"PC 189\", \"PC 190\", \"PC 191\", \"PC 192\", \"PC 193\", \"PC 194\", \"PC 195\", \"PC 196\", \"PC 197\", \"PC 198\", \"PC 199\", \"PC 200\", \"PC 201\", \"PC 202\", \"PC 203\", \"PC 204\", \"PC 205\", \"PC 206\", \"PC 207\", \"PC 208\", \"PC 209\", \"PC 210\", \"PC 211\", \"PC 212\", \"PC 213\", \"PC 214\", \"PC 215\", \"PC 216\", \"PC 217\", \"PC 218\", \"PC 219\", \"PC 220\", \"PC 221\", \"PC 222\", \"PC 223\", \"PC 224\", \"PC 225\", \"PC 226\", \"PC 227\", \"PC 228\", \"PC 229\", \"PC 230\", \"PC 231\", \"PC 232\", \"PC 233\", \"PC 234\", \"PC 235\", \"PC 236\", \"PC 237\", \"PC 238\", \"PC 239\", \"PC 240\", \"PC 241\", \"PC 242\", \"PC 243\", \"PC 244\", \"PC 245\", \"PC 246\", \"PC 247\", \"PC 248\", \"PC 249\", \"PC 250\", \"PC 251\", \"PC 252\", \"PC 253\", \"PC 254\", \"PC 255\", \"PC 256\", \"PC 257\", \"PC 258\", \"PC 259\", \"PC 260\", \"PC 261\", \"PC 262\", \"PC 263\", \"PC 264\", \"PC 265\", \"PC 266\", \"PC 267\", \"PC 268\", \"PC 269\", \"PC 270\", \"PC 271\", \"PC 272\", \"PC 273\", \"PC 274\", \"PC 275\", \"PC 276\", \"PC 277\", \"PC 278\", \"PC 279\", \"PC 280\", \"PC 281\", \"PC 282\", \"PC 283\", \"PC 284\", \"PC 285\", \"PC 286\", \"PC 287\", \"PC 288\", \"PC 289\", \"PC 290\", \"PC 291\", \"PC 292\", \"PC 293\", \"PC 294\", \"PC 295\", \"PC 296\", \"PC 297\", \"PC 298\", \"PC 299\", \"PC 300\", \"PC 301\", \"PC 302\", \"PC 303\", \"PC 304\", \"PC 305\", \"PC 306\", \"PC 307\", \"PC 308\", \"PC 309\", \"PC 310\", \"PC 311\", \"PC 312\", \"PC 313\", \"PC 314\", \"PC 315\", \"PC 316\", \"PC 317\", \"PC 318\", \"PC 319\", \"PC 320\", \"PC 321\", \"PC 322\", \"PC 323\", \"PC 324\", \"PC 325\", \"PC 326\", \"PC 327\", \"PC 328\", \"PC 329\", \"PC 330\", \"PC 331\", \"PC 332\", \"PC 333\", \"PC 334\", \"PC 335\", \"PC 336\", \"PC 337\", \"PC 338\", \"PC 339\", \"PC 340\", \"PC 341\", \"PC 342\", \"PC 343\", \"PC 344\", \"PC 345\", \"PC 346\", \"PC 347\", \"PC 348\", \"PC 349\", \"PC 350\", \"PC 351\", \"PC 352\", \"PC 353\", \"PC 354\", \"PC 355\", \"PC 356\", \"PC 357\", \"PC 358\", \"PC 359\", \"PC 360\", \"PC 361\", \"PC 362\", \"PC 363\", \"PC 364\", \"PC 365\", \"PC 366\", \"PC 367\", \"PC 368\", \"PC 369\", \"PC 370\", \"PC 371\", \"PC 372\", \"PC 373\", \"PC 374\", \"PC 375\", \"PC 376\", \"PC 377\", \"PC 378\", \"PC 379\", \"PC 380\", \"PC 381\", \"PC 382\", \"PC 383\", \"PC 384\", \"PC 385\", \"PC 386\", \"PC 387\", \"PC 388\", \"PC 389\", \"PC 390\", \"PC 391\", \"PC 392\", \"PC 393\", \"PC 394\", \"PC 395\", \"PC 396\", \"PC 397\", \"PC 398\", \"PC 399\", \"PC 400\", \"PC 401\", \"PC 402\", \"PC 403\", \"PC 404\", \"PC 405\", \"PC 406\", \"PC 407\", \"PC 408\", \"PC 409\", \"PC 410\", \"PC 411\", \"PC 412\", \"PC 413\", \"PC 414\", \"PC 415\", \"PC 416\", \"PC 417\", \"PC 418\", \"PC 419\", \"PC 420\", \"PC 421\", \"PC 422\", \"PC 423\", \"PC 424\", \"PC 425\", \"PC 426\", \"PC 427\", \"PC 428\", \"PC 429\", \"PC 430\", \"PC 431\", \"PC 432\", \"PC 433\", \"PC 434\", \"PC 435\", \"PC 436\", \"PC 437\", \"PC 438\", \"PC 439\", \"PC 440\", \"PC 441\", \"PC 442\", \"PC 443\", \"PC 444\", \"PC 445\", \"PC 446\", \"PC 447\", \"PC 448\", \"PC 449\", \"PC 450\", \"PC 451\", \"PC 452\", \"PC 453\", \"PC 454\", \"PC 455\", \"PC 456\", \"PC 457\", \"PC 458\", \"PC 459\", \"PC 460\", \"PC 461\", \"PC 462\", \"PC 463\", \"PC 464\", \"PC 465\", \"PC 466\", \"PC 467\", \"PC 468\", \"PC 469\", \"PC 470\", \"PC 471\", \"PC 472\", \"PC 473\", \"PC 474\", \"PC 475\", \"PC 476\", \"PC 477\", \"PC 478\", \"PC 479\", \"PC 480\", \"PC 481\", \"PC 482\", \"PC 483\", \"PC 484\", \"PC 485\", \"PC 486\", \"PC 487\", \"PC 488\", \"PC 489\", \"PC 490\", \"PC 491\", \"PC 492\", \"PC 493\", \"PC 494\", \"PC 495\", \"PC 496\", \"PC 497\", \"PC 498\", \"PC 499\", \"PC 500\", \"PC 501\", \"PC 502\", \"PC 503\", \"PC 504\", \"PC 505\", \"PC 506\", \"PC 507\", \"PC 508\", \"PC 509\", \"PC 510\", \"PC 511\", \"PC 512\", \"PC 513\", \"PC 514\", \"PC 515\", \"PC 516\", \"PC 517\", \"PC 518\", \"PC 519\", \"PC 520\", \"PC 521\", \"PC 522\", \"PC 523\", \"PC 524\", \"PC 525\", \"PC 526\", \"PC 527\", \"PC 528\", \"PC 529\", \"PC 530\", \"PC 531\", \"PC 532\", \"PC 533\", \"PC 534\", \"PC 535\", \"PC 536\", \"PC 537\", \"PC 538\", \"PC 539\", \"PC 540\", \"PC 541\", \"PC 542\", \"PC 543\", \"PC 544\", \"PC 545\", \"PC 546\", \"PC 547\", \"PC 548\", \"PC 549\", \"PC 550\", \"PC 551\", \"PC 552\", \"PC 553\", \"PC 554\", \"PC 555\", \"PC 556\", \"PC 557\", \"PC 558\", \"PC 559\", \"PC 560\", \"PC 561\", \"PC 562\", \"PC 563\", \"PC 564\", \"PC 565\", \"PC 566\", \"PC 567\", \"PC 568\", \"PC 569\", \"PC 570\", \"PC 571\", \"PC 572\", \"PC 573\", \"PC 574\", \"PC 575\", \"PC 576\", \"PC 577\", \"PC 578\", \"PC 579\", \"PC 580\", \"PC 581\", \"PC 582\", \"PC 583\", \"PC 584\", \"PC 585\", \"PC 586\", \"PC 587\", \"PC 588\", \"PC 589\", \"PC 590\", \"PC 591\", \"PC 592\", \"PC 593\", \"PC 594\", \"PC 595\", \"PC 596\", \"PC 597\", \"PC 598\", \"PC 599\", \"PC 600\", \"PC 601\", \"PC 602\", \"PC 603\", \"PC 604\", \"PC 605\", \"PC 606\", \"PC 607\", \"PC 608\", \"PC 609\", \"PC 610\", \"PC 611\", \"PC 612\", \"PC 613\", \"PC 614\", \"PC 615\", \"PC 616\", \"PC 617\", \"PC 618\", \"PC 619\", \"PC 620\", \"PC 621\", \"PC 622\", \"PC 623\", \"PC 624\", \"PC 625\", \"PC 626\", \"PC 627\", \"PC 628\", \"PC 629\", \"PC 630\", \"PC 631\", \"PC 632\", \"PC 633\", \"PC 634\", \"PC 635\", \"PC 636\", \"PC 637\", \"PC 638\", \"PC 639\", \"PC 640\", \"PC 641\", \"PC 642\", \"PC 643\", \"PC 644\", \"PC 645\", \"PC 646\", \"PC 647\", \"PC 648\", \"PC 649\", \"PC 650\", \"PC 651\", \"PC 652\", \"PC 653\", \"PC 654\", \"PC 655\", \"PC 656\", \"PC 657\", \"PC 658\", \"PC 659\", \"PC 660\", \"PC 661\", \"PC 662\", \"PC 663\", \"PC 664\", \"PC 665\", \"PC 666\", \"PC 667\", \"PC 668\", \"PC 669\", \"PC 670\", \"PC 671\", \"PC 672\", \"PC 673\", \"PC 674\", \"PC 675\", \"PC 676\", \"PC 677\", \"PC 678\", \"PC 679\", \"PC 680\", \"PC 681\", \"PC 682\", \"PC 683\", \"PC 684\", \"PC 685\", \"PC 686\", \"PC 687\", \"PC 688\", \"PC 689\", \"PC 690\", \"PC 691\", \"PC 692\", \"PC 693\", \"PC 694\", \"PC 695\", \"PC 696\", \"PC 697\", \"PC 698\", \"PC 699\", \"PC 700\", \"PC 701\", \"PC 702\", \"PC 703\", \"PC 704\", \"PC 705\", \"PC 706\", \"PC 707\", \"PC 708\", \"PC 709\", \"PC 710\", \"PC 711\", \"PC 712\", \"PC 713\", \"PC 714\", \"PC 715\", \"PC 716\", \"PC 717\", \"PC 718\", \"PC 719\", \"PC 720\", \"PC 721\", \"PC 722\", \"PC 723\", \"PC 724\", \"PC 725\", \"PC 726\", \"PC 727\", \"PC 728\", \"PC 729\", \"PC 730\", \"PC 731\", \"PC 732\", \"PC 733\", \"PC 734\", \"PC 735\", \"PC 736\", \"PC 737\", \"PC 738\", \"PC 739\", \"PC 740\", \"PC 741\", \"PC 742\", \"PC 743\", \"PC 744\", \"PC 745\", \"PC 746\", \"PC 747\", \"PC 748\", \"PC 749\", \"PC 750\", \"PC 751\", \"PC 752\", \"PC 753\", \"PC 754\", \"PC 755\", \"PC 756\", \"PC 757\", \"PC 758\", \"PC 759\", \"PC 760\", \"PC 761\", \"PC 762\", \"PC 763\", \"PC 764\", \"PC 765\", \"PC 766\", \"PC 767\", \"PC 768\", \"PC 769\", \"PC 770\", \"PC 771\", \"PC 772\", \"PC 773\", \"PC 774\", \"PC 775\", \"PC 776\", \"PC 777\", \"PC 778\", \"PC 779\", \"PC 780\", \"PC 781\", \"PC 782\", \"PC 783\", \"PC 784\"], \"y\": [9.704664359713888, 16.800588418808374, 22.969677181176486, 28.359096667729887, 33.22789369120473, 37.54012500649849, 40.81205496032024, 43.69595040652464, 46.45797980529533, 48.814980354934, 50.924169970000996, 52.94716105178833, 54.66297925131915, 56.35509068339043, 57.93373196389916, 59.41668457712042, 60.741245528024585, 62.01814289580257, 63.20540583539684, 64.3580895367477, 65.42425574383309, 66.43096911580751, 67.38454244265357, 68.29708618833114, 69.18049087999616, 70.01981002072027, 70.83238883018939, 71.61875491432265, 72.363488016634, 73.05434714429178, 73.71244091690382, 74.36058878685573, 74.96320381701013, 75.54978600486835, 76.11980747920471, 76.6634352499748, 77.16922166634606, 77.65708026995006, 78.13850961160838, 78.61077593790242, 79.0675228587842, 79.51235887052816, 79.93086019967394, 80.32907553836802, 80.71405014571822, 81.0891535326744, 81.45116238434063, 81.80275366116976, 82.14281186628807, 82.4646863333473, 82.78370338399554, 83.09650832314037, 83.39249099099732, 83.68144559061012, 83.96557598870221, 84.2370118001449, 84.50653325355515, 84.7650057990682, 85.01877639284683, 85.26355735244742, 85.50406348495544, 85.74332638642011, 85.97373487565606, 86.19526700710816, 86.40898782296465, 86.6162130625417, 86.81925573384589, 87.01603834944159, 87.20889094366244, 87.39752342224655, 87.58450048792722, 87.76558347070038, 87.94314557222891, 88.1180436452053, 88.28380186481431, 88.44769578688899, 88.609157900804, 88.7642743242466, 88.9118872982051, 89.05506336381052, 89.1971575914646, 89.33831078095065, 89.47848519542232, 89.6142215383099, 89.7480686807244, 89.88046501416069, 90.01062226425093, 90.13649535379415, 90.25932351354234, 90.3809079992643, 90.49794246115557, 90.61281605166636, 90.72606023472898, 90.83694587461494, 90.94594768362207, 91.05287091767234, 91.15706689215087, 91.26107370768165, 91.3623299877357, 91.46285724395082, 91.56125897319798, 91.65622759572733, 91.75036168104954, 91.84197831994379, 91.93276338782567, 92.02245061262595, 92.10898974229245, 92.19450695441307, 92.27906894854779, 92.36131851143068, 92.44047693682379, 92.51907080626215, 92.59753147671401, 92.6744146320085, 92.75081618146474, 92.82612501748596, 92.89980331016854, 92.97251650295175, 93.04448166732922, 93.11516329574509, 93.18470573980028, 93.25392185132726, 93.32225218656697, 93.38965824171136, 93.45634592305616, 93.52087249681655, 93.58443191165225, 93.64759653961292, 93.70988990800225, 93.77041893236165, 93.83077779918644, 93.89022589636376, 93.94905667009768, 94.00770867581848, 94.06584276497696, 94.12352589816308, 94.18006280944857, 94.23553925721104, 94.28905628923621, 94.34164882596906, 94.39415814725682, 94.44518384059977, 94.49548091969676, 94.54558870591632, 94.59545998867483, 94.64456697810171, 94.69312073606845, 94.7414053695528, 94.78880675165485, 94.83564188145836, 94.8823017771185, 94.92863456560555, 94.97456393815953, 95.01960192613038, 95.06448266584884, 95.10875365848221, 95.1524210920029, 95.19516594258756, 95.2376638646023, 95.27986510464166, 95.32141645808909, 95.36238016414215, 95.40246254171977, 95.44225077003524, 95.48165884374002, 95.52070820060929, 95.55929345873606, 95.59727111372246, 95.6351610300652, 95.6725549644378, 95.70949642118724, 95.74601149002234, 95.7823928169557, 95.81838027820083, 95.85384450097774, 95.88913429787792, 95.92386314266986, 95.958458866936, 95.9926035729305, 96.02636814271713, 96.06007754332006, 96.09310024599397, 96.12593573177561, 96.15852646655009, 96.19082091902293, 96.22294783216316, 96.25467776110929, 96.28629526090513, 96.31738951550199, 96.3483432032713, 96.37893983966687, 96.40926731605876, 96.4395083461272, 96.46966521915725, 96.49933593991602, 96.52891059681778, 96.5582577701243, 96.58752502085426, 96.61630024873087, 96.64473477010526, 96.67293139572227, 96.70083842135139, 96.72841187764327, 96.75565933862424, 96.78260286499933, 96.80937359913341, 96.83588560807378, 96.86231832194912, 96.88850661125947, 96.91445170279411, 96.94030739459915, 96.96599967491895, 96.99147337348354, 97.01675457229655, 97.04198355533465, 97.06693984795648, 97.09179151145435, 97.11639900641067, 97.14079449915968, 97.16498080833772, 97.18907762304275, 97.21312201556192, 97.23694899720432, 97.26063433623916, 97.28389214513392, 97.30702303782503, 97.33003584431381, 97.3528445190116, 97.37560285319056, 97.39788047474185, 97.42006677592103, 97.44211101044112, 97.46389766826618, 97.48556331265948, 97.50707970601441, 97.52849919313361, 97.54978470622649, 97.57082195471423, 97.59179745733822, 97.61249360244149, 97.63296599835985, 97.65339312436367, 97.67352454952413, 97.69362303195022, 97.71352268756863, 97.73328575183879, 97.75286849651184, 97.77224132038299, 97.79152716045884, 97.81070442612378, 97.82985861876344, 97.8487663897674, 97.86756764657231, 97.88620687584762, 97.90479162740934, 97.92325343247605, 97.94162301660751, 97.95993763468124, 97.97812569656784, 97.99611232981839, 98.01386790490533, 98.03153677835752, 98.04913299272316, 98.06652127966461, 98.08386413884476, 98.10112867569688, 98.11826723926585, 98.13527088639066, 98.15220093780077, 98.16900148464256, 98.1856936598304, 98.20233888912114, 98.21875945073496, 98.2351076180398, 98.25137342346866, 98.26756247311394, 98.28365160015417, 98.29963598453558, 98.31551927144977, 98.33125445147743, 98.34692822514565, 98.36241793866914, 98.37779883813401, 98.3931056320335, 98.40830951330936, 98.42331057972957, 98.43827707287092, 98.45309999632694, 98.46786738944382, 98.48248012761206, 98.49694536427764, 98.51126874492456, 98.52554104312738, 98.53974799100855, 98.5539228907991, 98.56797210862995, 98.58179587183659, 98.59559309619054, 98.60927722267263, 98.62287476125923, 98.6364542831316, 98.6499052009417, 98.66326692299519, 98.67650120339057, 98.68957138428111, 98.70259033882554, 98.71550661762952, 98.72831778065016, 98.74106934286625, 98.7537911285177, 98.76642499733317, 98.77901100478523, 98.79148407802805, 98.80384030880471, 98.8161024831791, 98.82825920680233, 98.84036191384399, 98.85235865983353, 98.86430087515521, 98.8761957524363, 98.88798296634795, 98.8996889631474, 98.91133845459055, 98.92294835873409, 98.93440141415735, 98.94582311052436, 98.95706376543781, 98.96819129900472, 98.97924530777586, 98.99028838329114, 99.00129426354096, 99.01219174685416, 99.02302405358522, 99.03378362351845, 99.04448406057863, 99.05510455700885, 99.06569745700877, 99.0762024392913, 99.08654449487925, 99.09676951807991, 99.10697410272942, 99.11705867923197, 99.12708514991705, 99.13704492597088, 99.14698221932625, 99.15679471658491, 99.16655423069946, 99.17623734991669, 99.18578979172918, 99.19524427549271, 99.20462409754326, 99.2139963715142, 99.22324567701148, 99.23240442188109, 99.24154409868737, 99.25061151743894, 99.25961903136107, 99.26855607898422, 99.27747167501, 99.2862978140153, 99.29503060553213, 99.30366156491633, 99.31221910421482, 99.32073487930793, 99.32919508634231, 99.33752636832634, 99.34582416549006, 99.35407403566548, 99.36226518707612, 99.37037422402322, 99.37846453894105, 99.38642540276417, 99.39437223530047, 99.40223484778369, 99.41004096143021, 99.41778348366172, 99.42544250839406, 99.43302290004043, 99.44048386442144, 99.44786844066273, 99.45522535320862, 99.46250691479477, 99.46977831631683, 99.47698498748377, 99.48412662777496, 99.4912072063956, 99.49817237222884, 99.50509687475785, 99.51192683687577, 99.51872067621827, 99.52542653576259, 99.53204998108396, 99.53857424362636, 99.5449944929675, 99.55136553249754, 99.55771089095732, 99.56391416694095, 99.57004282583387, 99.57607472825255, 99.58206755674023, 99.58800436101775, 99.59387735147548, 99.59973941997235, 99.60547804147458, 99.61115058121506, 99.61678796273145, 99.62234961180243, 99.62783974069511, 99.63331362227437, 99.63876092245374, 99.64409393756125, 99.64936949742032, 99.65462426624693, 99.65984408998251, 99.66502929828424, 99.67013078699999, 99.67516889093866, 99.6801444336056, 99.68505117208038, 99.68992125447619, 99.6947154714379, 99.69943629449239, 99.70410236386732, 99.7087466252953, 99.71330678456538, 99.71779772709093, 99.72216907485961, 99.72646172837092, 99.73072262870046, 99.73496119003639, 99.73917861382239, 99.74335708729018, 99.74749579081296, 99.75158040897468, 99.75560909361606, 99.7594679678901, 99.76329316761857, 99.7671073570228, 99.77089574077833, 99.77462812250742, 99.77833554702634, 99.78199456418305, 99.78557105235308, 99.78910684765111, 99.79263215799915, 99.79611915776127, 99.7995742139968, 99.80301257108003, 99.80635282704904, 99.80965274502034, 99.81287259286879, 99.81606652815412, 99.81923060914565, 99.82233191500174, 99.82537283809616, 99.8283884405316, 99.83137906273954, 99.83430034765958, 99.83718699436793, 99.84003883947435, 99.8428453465662, 99.845636086627, 99.84838781876273, 99.85108235152704, 99.85365961582318, 99.8561888221768, 99.8587051192801, 99.86118794525038, 99.86365670159562, 99.86609234796089, 99.86852376026137, 99.87094866196631, 99.8733212435031, 99.87565637769599, 99.87797808590778, 99.88022992645604, 99.88246644879239, 99.88467829362835, 99.88682153218777, 99.88895107766622, 99.89105781483626, 99.89314344136588, 99.89518115229056, 99.89719012609692, 99.89917657540687, 99.90113902802977, 99.90309049583145, 99.90498645833087, 99.90683140664098, 99.90865006745919, 99.9104603164009, 99.91225604952527, 99.91401489173124, 99.91575588715611, 99.91739172316846, 99.91900903270053, 99.92061986969284, 99.92221026361482, 99.92376417411762, 99.9252847684116, 99.92680147239211, 99.92829942382481, 99.92977527092782, 99.93123309939281, 99.93266856659626, 99.9340862743334, 99.93548248874853, 99.9368614607783, 99.93822891801015, 99.93956223147319, 99.94087262586498, 99.94212749902941, 99.94336563446146, 99.9445841626974, 99.94578431723785, 99.94697557294953, 99.94815323466055, 99.94932630909952, 99.95046419024823, 99.95159587507236, 99.95272051132434, 99.9538207722528, 99.95491447502536, 99.95597148232595, 99.95702532274315, 99.95804852577088, 99.95905071748506, 99.96000820396293, 99.96094545225084, 99.96187148679658, 99.9627937123409, 99.96368087774256, 99.96456185765292, 99.96542108696596, 99.9662371055002, 99.96703409677355, 99.96782081590965, 99.96859420974806, 99.96935859856889, 99.97011635192477, 99.97086954640028, 99.97160640737553, 99.97233332825525, 99.97304819462157, 99.97374435710746, 99.9744324688394, 99.97510400514399, 99.97576958674011, 99.97642338791242, 99.97707039930177, 99.97768438963936, 99.97827712862774, 99.97884985219275, 99.97941757658268, 99.97997307466991, 99.98050801264141, 99.9810350856299, 99.9815533409017, 99.9820572632686, 99.9825568166921, 99.98305008580677, 99.98354017344215, 99.98402123774925, 99.98449083922857, 99.9849531680658, 99.98540862663086, 99.98582845509361, 99.98624694491848, 99.98664821779121, 99.98704837334988, 99.98744288666295, 99.98782286207143, 99.98820094755285, 99.98853216533888, 99.98885595302845, 99.98917721179977, 99.98949473108264, 99.98980668902652, 99.99011490539446, 99.9904174872144, 99.99071870138432, 99.99101577171857, 99.99131136509538, 99.99160382347857, 99.99188420044094, 99.99214704598705, 99.99240203957916, 99.99263820995785, 99.99286975682435, 99.99309605317818, 99.99332052794396, 99.99354129707251, 99.9937564125079, 99.99397107635086, 99.99418128030302, 99.99438545738646, 99.99457337227729, 99.99475987854855, 99.99494509838878, 99.99512954430163, 99.99530958133451, 99.9954850144011, 99.99564685808012, 99.99580739879097, 99.99595774604616, 99.99610385182422, 99.99624518208316, 99.99638401694983, 99.99651583737958, 99.99664616131747, 99.99677462592786, 99.99689930981614, 99.99701123014066, 99.99711907075026, 99.99722386568598, 99.99732802394746, 99.99743159875683, 99.99752972118775, 99.997626361699, 99.99771981096998, 99.99781138552571, 99.9979023640495, 99.99799226994921, 99.99807980863777, 99.99816312321674, 99.99824073634873, 99.99831523285076, 99.99838741685141, 99.99845408023916, 99.9985200532257, 99.99858374392095, 99.99864629998264, 99.99870883776961, 99.99876793034491, 99.99882621895405, 99.99888290727041, 99.99893900380516, 99.99899182532609, 99.99904405010982, 99.99909179824387, 99.9991389647981, 99.99918557842855, 99.99922880596887, 99.99927084965675, 99.99931149706964, 99.99934988584135, 99.99938609884298, 99.99942176503508, 99.99945299669011, 99.99948267976976, 99.99951052127747, 99.99953778935289, 99.99956353784931, 99.99958909280299, 99.99961322161217, 99.99963679218712, 99.99965978627482, 99.99968232149733, 99.99970382104661, 99.99972407466633, 99.99974421866109, 99.99976383548865, 99.99978150952388, 99.99979863239395, 99.9998137317399, 99.99982870356861, 99.99984236369187, 99.99985589415135, 99.99986869953518, 99.99987940450735, 99.99988885347132, 99.99989763738984, 99.99990596389475, 99.99991413199677, 99.99992098087226, 99.99992770456, 99.99993412561723, 99.99994008450456, 99.99994562476354, 99.99995028594378, 99.9999548794822, 99.99995894470878, 99.99996288054915, 99.99996648510545, 99.9999700544871, 99.99997329470388, 99.99997638231692, 99.99997938714769, 99.99998227786394, 99.99998468036948, 99.99998656503193, 99.99998833761123, 99.99999000060134, 99.99999162107582, 99.99999273609028, 99.99999376677113, 99.99999477661306, 99.99999564108428, 99.99999643688462, 99.9999971285218, 99.99999781704565, 99.99999836026268, 99.99999885684886, 99.99999922667102, 99.99999952870562, 99.9999997227134, 99.99999980945177, 99.99999988027068, 99.99999994949681, 99.99999997484746, 99.99999999846939, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999], \"name\": \"cumulative explained variance\"}], {\"yaxis\": {\"title\": \"explained variance in percent\"}, \"title\": \"Cumulative Explained variance by different principal components 1 - 784\"}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<div id=\"67d6e4e6-5ea2-48b8-b7a8-c1a58d6b9a41\" style=\"height: 525px; width: 100%;\" class=\"plotly-graph-div\"></div><script type=\"text/javascript\">require([\"plotly\"], function(Plotly) { window.PLOTLYENV=window.PLOTLYENV || {};window.PLOTLYENV.BASE_URL=\"https://plot.ly\";Plotly.newPlot(\"67d6e4e6-5ea2-48b8-b7a8-c1a58d6b9a41\", [{\"type\": \"scatter\", \"x\": [\"PC 1\", \"PC 2\", \"PC 3\", \"PC 4\", \"PC 5\", \"PC 6\", \"PC 7\", \"PC 8\", \"PC 9\", \"PC 10\", \"PC 11\", \"PC 12\", \"PC 13\", \"PC 14\", \"PC 15\", \"PC 16\", \"PC 17\", \"PC 18\", \"PC 19\", \"PC 20\", \"PC 21\", \"PC 22\", \"PC 23\", \"PC 24\", \"PC 25\", \"PC 26\", \"PC 27\", \"PC 28\", \"PC 29\", \"PC 30\", \"PC 31\", \"PC 32\", \"PC 33\", \"PC 34\", \"PC 35\", \"PC 36\", \"PC 37\", \"PC 38\", \"PC 39\", \"PC 40\", \"PC 41\", \"PC 42\", \"PC 43\", \"PC 44\", \"PC 45\", \"PC 46\", \"PC 47\", \"PC 48\", \"PC 49\", \"PC 50\", \"PC 51\", \"PC 52\", \"PC 53\", \"PC 54\", \"PC 55\", \"PC 56\", \"PC 57\", \"PC 58\", \"PC 59\", \"PC 60\", \"PC 61\", \"PC 62\", \"PC 63\", \"PC 64\", \"PC 65\", \"PC 66\", \"PC 67\", \"PC 68\", \"PC 69\", \"PC 70\", \"PC 71\", \"PC 72\", \"PC 73\", \"PC 74\", \"PC 75\", \"PC 76\", \"PC 77\", \"PC 78\", \"PC 79\", \"PC 80\", \"PC 81\", \"PC 82\", \"PC 83\", \"PC 84\", \"PC 85\", \"PC 86\", \"PC 87\", \"PC 88\", \"PC 89\", \"PC 90\", \"PC 91\", \"PC 92\", \"PC 93\", \"PC 94\", \"PC 95\", \"PC 96\", \"PC 97\", \"PC 98\", \"PC 99\", \"PC 100\", \"PC 101\", \"PC 102\", \"PC 103\", \"PC 104\", \"PC 105\", \"PC 106\", \"PC 107\", \"PC 108\", \"PC 109\", \"PC 110\", \"PC 111\", \"PC 112\", \"PC 113\", \"PC 114\", \"PC 115\", \"PC 116\", \"PC 117\", \"PC 118\", \"PC 119\", \"PC 120\", \"PC 121\", \"PC 122\", \"PC 123\", \"PC 124\", \"PC 125\", \"PC 126\", \"PC 127\", \"PC 128\", \"PC 129\", \"PC 130\", \"PC 131\", \"PC 132\", \"PC 133\", \"PC 134\", \"PC 135\", \"PC 136\", \"PC 137\", \"PC 138\", \"PC 139\", \"PC 140\", \"PC 141\", \"PC 142\", \"PC 143\", \"PC 144\", \"PC 145\", \"PC 146\", \"PC 147\", \"PC 148\", \"PC 149\", \"PC 150\", \"PC 151\", \"PC 152\", \"PC 153\", \"PC 154\", \"PC 155\", \"PC 156\", \"PC 157\", \"PC 158\", \"PC 159\", \"PC 160\", \"PC 161\", \"PC 162\", \"PC 163\", \"PC 164\", \"PC 165\", \"PC 166\", \"PC 167\", \"PC 168\", \"PC 169\", \"PC 170\", \"PC 171\", \"PC 172\", \"PC 173\", \"PC 174\", \"PC 175\", \"PC 176\", \"PC 177\", \"PC 178\", \"PC 179\", \"PC 180\", \"PC 181\", \"PC 182\", \"PC 183\", \"PC 184\", \"PC 185\", \"PC 186\", \"PC 187\", \"PC 188\", \"PC 189\", \"PC 190\", \"PC 191\", \"PC 192\", \"PC 193\", \"PC 194\", \"PC 195\", \"PC 196\", \"PC 197\", \"PC 198\", \"PC 199\", \"PC 200\", \"PC 201\", \"PC 202\", \"PC 203\", \"PC 204\", \"PC 205\", \"PC 206\", \"PC 207\", \"PC 208\", \"PC 209\", \"PC 210\", \"PC 211\", \"PC 212\", \"PC 213\", \"PC 214\", \"PC 215\", \"PC 216\", \"PC 217\", \"PC 218\", \"PC 219\", \"PC 220\", \"PC 221\", \"PC 222\", \"PC 223\", \"PC 224\", \"PC 225\", \"PC 226\", \"PC 227\", \"PC 228\", \"PC 229\", \"PC 230\", \"PC 231\", \"PC 232\", \"PC 233\", \"PC 234\", \"PC 235\", \"PC 236\", \"PC 237\", \"PC 238\", \"PC 239\", \"PC 240\", \"PC 241\", \"PC 242\", \"PC 243\", \"PC 244\", \"PC 245\", \"PC 246\", \"PC 247\", \"PC 248\", \"PC 249\", \"PC 250\", \"PC 251\", \"PC 252\", \"PC 253\", \"PC 254\", \"PC 255\", \"PC 256\", \"PC 257\", \"PC 258\", \"PC 259\", \"PC 260\", \"PC 261\", \"PC 262\", \"PC 263\", \"PC 264\", \"PC 265\", \"PC 266\", \"PC 267\", \"PC 268\", \"PC 269\", \"PC 270\", \"PC 271\", \"PC 272\", \"PC 273\", \"PC 274\", \"PC 275\", \"PC 276\", \"PC 277\", \"PC 278\", \"PC 279\", \"PC 280\", \"PC 281\", \"PC 282\", \"PC 283\", \"PC 284\", \"PC 285\", \"PC 286\", \"PC 287\", \"PC 288\", \"PC 289\", \"PC 290\", \"PC 291\", \"PC 292\", \"PC 293\", \"PC 294\", \"PC 295\", \"PC 296\", \"PC 297\", \"PC 298\", \"PC 299\", \"PC 300\", \"PC 301\", \"PC 302\", \"PC 303\", \"PC 304\", \"PC 305\", \"PC 306\", \"PC 307\", \"PC 308\", \"PC 309\", \"PC 310\", \"PC 311\", \"PC 312\", \"PC 313\", \"PC 314\", \"PC 315\", \"PC 316\", \"PC 317\", \"PC 318\", \"PC 319\", \"PC 320\", \"PC 321\", \"PC 322\", \"PC 323\", \"PC 324\", \"PC 325\", \"PC 326\", \"PC 327\", \"PC 328\", \"PC 329\", \"PC 330\", \"PC 331\", \"PC 332\", \"PC 333\", \"PC 334\", \"PC 335\", \"PC 336\", \"PC 337\", \"PC 338\", \"PC 339\", \"PC 340\", \"PC 341\", \"PC 342\", \"PC 343\", \"PC 344\", \"PC 345\", \"PC 346\", \"PC 347\", \"PC 348\", \"PC 349\", \"PC 350\", \"PC 351\", \"PC 352\", \"PC 353\", \"PC 354\", \"PC 355\", \"PC 356\", \"PC 357\", \"PC 358\", \"PC 359\", \"PC 360\", \"PC 361\", \"PC 362\", \"PC 363\", \"PC 364\", \"PC 365\", \"PC 366\", \"PC 367\", \"PC 368\", \"PC 369\", \"PC 370\", \"PC 371\", \"PC 372\", \"PC 373\", \"PC 374\", \"PC 375\", \"PC 376\", \"PC 377\", \"PC 378\", \"PC 379\", \"PC 380\", \"PC 381\", \"PC 382\", \"PC 383\", \"PC 384\", \"PC 385\", \"PC 386\", \"PC 387\", \"PC 388\", \"PC 389\", \"PC 390\", \"PC 391\", \"PC 392\", \"PC 393\", \"PC 394\", \"PC 395\", \"PC 396\", \"PC 397\", \"PC 398\", \"PC 399\", \"PC 400\", \"PC 401\", \"PC 402\", \"PC 403\", \"PC 404\", \"PC 405\", \"PC 406\", \"PC 407\", \"PC 408\", \"PC 409\", \"PC 410\", \"PC 411\", \"PC 412\", \"PC 413\", \"PC 414\", \"PC 415\", \"PC 416\", \"PC 417\", \"PC 418\", \"PC 419\", \"PC 420\", \"PC 421\", \"PC 422\", \"PC 423\", \"PC 424\", \"PC 425\", \"PC 426\", \"PC 427\", \"PC 428\", \"PC 429\", \"PC 430\", \"PC 431\", \"PC 432\", \"PC 433\", \"PC 434\", \"PC 435\", \"PC 436\", \"PC 437\", \"PC 438\", \"PC 439\", \"PC 440\", \"PC 441\", \"PC 442\", \"PC 443\", \"PC 444\", \"PC 445\", \"PC 446\", \"PC 447\", \"PC 448\", \"PC 449\", \"PC 450\", \"PC 451\", \"PC 452\", \"PC 453\", \"PC 454\", \"PC 455\", \"PC 456\", \"PC 457\", \"PC 458\", \"PC 459\", \"PC 460\", \"PC 461\", \"PC 462\", \"PC 463\", \"PC 464\", \"PC 465\", \"PC 466\", \"PC 467\", \"PC 468\", \"PC 469\", \"PC 470\", \"PC 471\", \"PC 472\", \"PC 473\", \"PC 474\", \"PC 475\", \"PC 476\", \"PC 477\", \"PC 478\", \"PC 479\", \"PC 480\", \"PC 481\", \"PC 482\", \"PC 483\", \"PC 484\", \"PC 485\", \"PC 486\", \"PC 487\", \"PC 488\", \"PC 489\", \"PC 490\", \"PC 491\", \"PC 492\", \"PC 493\", \"PC 494\", \"PC 495\", \"PC 496\", \"PC 497\", \"PC 498\", \"PC 499\", \"PC 500\", \"PC 501\", \"PC 502\", \"PC 503\", \"PC 504\", \"PC 505\", \"PC 506\", \"PC 507\", \"PC 508\", \"PC 509\", \"PC 510\", \"PC 511\", \"PC 512\", \"PC 513\", \"PC 514\", \"PC 515\", \"PC 516\", \"PC 517\", \"PC 518\", \"PC 519\", \"PC 520\", \"PC 521\", \"PC 522\", \"PC 523\", \"PC 524\", \"PC 525\", \"PC 526\", \"PC 527\", \"PC 528\", \"PC 529\", \"PC 530\", \"PC 531\", \"PC 532\", \"PC 533\", \"PC 534\", \"PC 535\", \"PC 536\", \"PC 537\", \"PC 538\", \"PC 539\", \"PC 540\", \"PC 541\", \"PC 542\", \"PC 543\", \"PC 544\", \"PC 545\", \"PC 546\", \"PC 547\", \"PC 548\", \"PC 549\", \"PC 550\", \"PC 551\", \"PC 552\", \"PC 553\", \"PC 554\", \"PC 555\", \"PC 556\", \"PC 557\", \"PC 558\", \"PC 559\", \"PC 560\", \"PC 561\", \"PC 562\", \"PC 563\", \"PC 564\", \"PC 565\", \"PC 566\", \"PC 567\", \"PC 568\", \"PC 569\", \"PC 570\", \"PC 571\", \"PC 572\", \"PC 573\", \"PC 574\", \"PC 575\", \"PC 576\", \"PC 577\", \"PC 578\", \"PC 579\", \"PC 580\", \"PC 581\", \"PC 582\", \"PC 583\", \"PC 584\", \"PC 585\", \"PC 586\", \"PC 587\", \"PC 588\", \"PC 589\", \"PC 590\", \"PC 591\", \"PC 592\", \"PC 593\", \"PC 594\", \"PC 595\", \"PC 596\", \"PC 597\", \"PC 598\", \"PC 599\", \"PC 600\", \"PC 601\", \"PC 602\", \"PC 603\", \"PC 604\", \"PC 605\", \"PC 606\", \"PC 607\", \"PC 608\", \"PC 609\", \"PC 610\", \"PC 611\", \"PC 612\", \"PC 613\", \"PC 614\", \"PC 615\", \"PC 616\", \"PC 617\", \"PC 618\", \"PC 619\", \"PC 620\", \"PC 621\", \"PC 622\", \"PC 623\", \"PC 624\", \"PC 625\", \"PC 626\", \"PC 627\", \"PC 628\", \"PC 629\", \"PC 630\", \"PC 631\", \"PC 632\", \"PC 633\", \"PC 634\", \"PC 635\", \"PC 636\", \"PC 637\", \"PC 638\", \"PC 639\", \"PC 640\", \"PC 641\", \"PC 642\", \"PC 643\", \"PC 644\", \"PC 645\", \"PC 646\", \"PC 647\", \"PC 648\", \"PC 649\", \"PC 650\", \"PC 651\", \"PC 652\", \"PC 653\", \"PC 654\", \"PC 655\", \"PC 656\", \"PC 657\", \"PC 658\", \"PC 659\", \"PC 660\", \"PC 661\", \"PC 662\", \"PC 663\", \"PC 664\", \"PC 665\", \"PC 666\", \"PC 667\", \"PC 668\", \"PC 669\", \"PC 670\", \"PC 671\", \"PC 672\", \"PC 673\", \"PC 674\", \"PC 675\", \"PC 676\", \"PC 677\", \"PC 678\", \"PC 679\", \"PC 680\", \"PC 681\", \"PC 682\", \"PC 683\", \"PC 684\", \"PC 685\", \"PC 686\", \"PC 687\", \"PC 688\", \"PC 689\", \"PC 690\", \"PC 691\", \"PC 692\", \"PC 693\", \"PC 694\", \"PC 695\", \"PC 696\", \"PC 697\", \"PC 698\", \"PC 699\", \"PC 700\", \"PC 701\", \"PC 702\", \"PC 703\", \"PC 704\", \"PC 705\", \"PC 706\", \"PC 707\", \"PC 708\", \"PC 709\", \"PC 710\", \"PC 711\", \"PC 712\", \"PC 713\", \"PC 714\", \"PC 715\", \"PC 716\", \"PC 717\", \"PC 718\", \"PC 719\", \"PC 720\", \"PC 721\", \"PC 722\", \"PC 723\", \"PC 724\", \"PC 725\", \"PC 726\", \"PC 727\", \"PC 728\", \"PC 729\", \"PC 730\", \"PC 731\", \"PC 732\", \"PC 733\", \"PC 734\", \"PC 735\", \"PC 736\", \"PC 737\", \"PC 738\", \"PC 739\", \"PC 740\", \"PC 741\", \"PC 742\", \"PC 743\", \"PC 744\", \"PC 745\", \"PC 746\", \"PC 747\", \"PC 748\", \"PC 749\", \"PC 750\", \"PC 751\", \"PC 752\", \"PC 753\", \"PC 754\", \"PC 755\", \"PC 756\", \"PC 757\", \"PC 758\", \"PC 759\", \"PC 760\", \"PC 761\", \"PC 762\", \"PC 763\", \"PC 764\", \"PC 765\", \"PC 766\", \"PC 767\", \"PC 768\", \"PC 769\", \"PC 770\", \"PC 771\", \"PC 772\", \"PC 773\", \"PC 774\", \"PC 775\", \"PC 776\", \"PC 777\", \"PC 778\", \"PC 779\", \"PC 780\", \"PC 781\", \"PC 782\", \"PC 783\", \"PC 784\"], \"y\": [9.704664359713888, 16.800588418808374, 22.969677181176486, 28.359096667729887, 33.22789369120473, 37.54012500649849, 40.81205496032024, 43.69595040652464, 46.45797980529533, 48.814980354934, 50.924169970000996, 52.94716105178833, 54.66297925131915, 56.35509068339043, 57.93373196389916, 59.41668457712042, 60.741245528024585, 62.01814289580257, 63.20540583539684, 64.3580895367477, 65.42425574383309, 66.43096911580751, 67.38454244265357, 68.29708618833114, 69.18049087999616, 70.01981002072027, 70.83238883018939, 71.61875491432265, 72.363488016634, 73.05434714429178, 73.71244091690382, 74.36058878685573, 74.96320381701013, 75.54978600486835, 76.11980747920471, 76.6634352499748, 77.16922166634606, 77.65708026995006, 78.13850961160838, 78.61077593790242, 79.0675228587842, 79.51235887052816, 79.93086019967394, 80.32907553836802, 80.71405014571822, 81.0891535326744, 81.45116238434063, 81.80275366116976, 82.14281186628807, 82.4646863333473, 82.78370338399554, 83.09650832314037, 83.39249099099732, 83.68144559061012, 83.96557598870221, 84.2370118001449, 84.50653325355515, 84.7650057990682, 85.01877639284683, 85.26355735244742, 85.50406348495544, 85.74332638642011, 85.97373487565606, 86.19526700710816, 86.40898782296465, 86.6162130625417, 86.81925573384589, 87.01603834944159, 87.20889094366244, 87.39752342224655, 87.58450048792722, 87.76558347070038, 87.94314557222891, 88.1180436452053, 88.28380186481431, 88.44769578688899, 88.609157900804, 88.7642743242466, 88.9118872982051, 89.05506336381052, 89.1971575914646, 89.33831078095065, 89.47848519542232, 89.6142215383099, 89.7480686807244, 89.88046501416069, 90.01062226425093, 90.13649535379415, 90.25932351354234, 90.3809079992643, 90.49794246115557, 90.61281605166636, 90.72606023472898, 90.83694587461494, 90.94594768362207, 91.05287091767234, 91.15706689215087, 91.26107370768165, 91.3623299877357, 91.46285724395082, 91.56125897319798, 91.65622759572733, 91.75036168104954, 91.84197831994379, 91.93276338782567, 92.02245061262595, 92.10898974229245, 92.19450695441307, 92.27906894854779, 92.36131851143068, 92.44047693682379, 92.51907080626215, 92.59753147671401, 92.6744146320085, 92.75081618146474, 92.82612501748596, 92.89980331016854, 92.97251650295175, 93.04448166732922, 93.11516329574509, 93.18470573980028, 93.25392185132726, 93.32225218656697, 93.38965824171136, 93.45634592305616, 93.52087249681655, 93.58443191165225, 93.64759653961292, 93.70988990800225, 93.77041893236165, 93.83077779918644, 93.89022589636376, 93.94905667009768, 94.00770867581848, 94.06584276497696, 94.12352589816308, 94.18006280944857, 94.23553925721104, 94.28905628923621, 94.34164882596906, 94.39415814725682, 94.44518384059977, 94.49548091969676, 94.54558870591632, 94.59545998867483, 94.64456697810171, 94.69312073606845, 94.7414053695528, 94.78880675165485, 94.83564188145836, 94.8823017771185, 94.92863456560555, 94.97456393815953, 95.01960192613038, 95.06448266584884, 95.10875365848221, 95.1524210920029, 95.19516594258756, 95.2376638646023, 95.27986510464166, 95.32141645808909, 95.36238016414215, 95.40246254171977, 95.44225077003524, 95.48165884374002, 95.52070820060929, 95.55929345873606, 95.59727111372246, 95.6351610300652, 95.6725549644378, 95.70949642118724, 95.74601149002234, 95.7823928169557, 95.81838027820083, 95.85384450097774, 95.88913429787792, 95.92386314266986, 95.958458866936, 95.9926035729305, 96.02636814271713, 96.06007754332006, 96.09310024599397, 96.12593573177561, 96.15852646655009, 96.19082091902293, 96.22294783216316, 96.25467776110929, 96.28629526090513, 96.31738951550199, 96.3483432032713, 96.37893983966687, 96.40926731605876, 96.4395083461272, 96.46966521915725, 96.49933593991602, 96.52891059681778, 96.5582577701243, 96.58752502085426, 96.61630024873087, 96.64473477010526, 96.67293139572227, 96.70083842135139, 96.72841187764327, 96.75565933862424, 96.78260286499933, 96.80937359913341, 96.83588560807378, 96.86231832194912, 96.88850661125947, 96.91445170279411, 96.94030739459915, 96.96599967491895, 96.99147337348354, 97.01675457229655, 97.04198355533465, 97.06693984795648, 97.09179151145435, 97.11639900641067, 97.14079449915968, 97.16498080833772, 97.18907762304275, 97.21312201556192, 97.23694899720432, 97.26063433623916, 97.28389214513392, 97.30702303782503, 97.33003584431381, 97.3528445190116, 97.37560285319056, 97.39788047474185, 97.42006677592103, 97.44211101044112, 97.46389766826618, 97.48556331265948, 97.50707970601441, 97.52849919313361, 97.54978470622649, 97.57082195471423, 97.59179745733822, 97.61249360244149, 97.63296599835985, 97.65339312436367, 97.67352454952413, 97.69362303195022, 97.71352268756863, 97.73328575183879, 97.75286849651184, 97.77224132038299, 97.79152716045884, 97.81070442612378, 97.82985861876344, 97.8487663897674, 97.86756764657231, 97.88620687584762, 97.90479162740934, 97.92325343247605, 97.94162301660751, 97.95993763468124, 97.97812569656784, 97.99611232981839, 98.01386790490533, 98.03153677835752, 98.04913299272316, 98.06652127966461, 98.08386413884476, 98.10112867569688, 98.11826723926585, 98.13527088639066, 98.15220093780077, 98.16900148464256, 98.1856936598304, 98.20233888912114, 98.21875945073496, 98.2351076180398, 98.25137342346866, 98.26756247311394, 98.28365160015417, 98.29963598453558, 98.31551927144977, 98.33125445147743, 98.34692822514565, 98.36241793866914, 98.37779883813401, 98.3931056320335, 98.40830951330936, 98.42331057972957, 98.43827707287092, 98.45309999632694, 98.46786738944382, 98.48248012761206, 98.49694536427764, 98.51126874492456, 98.52554104312738, 98.53974799100855, 98.5539228907991, 98.56797210862995, 98.58179587183659, 98.59559309619054, 98.60927722267263, 98.62287476125923, 98.6364542831316, 98.6499052009417, 98.66326692299519, 98.67650120339057, 98.68957138428111, 98.70259033882554, 98.71550661762952, 98.72831778065016, 98.74106934286625, 98.7537911285177, 98.76642499733317, 98.77901100478523, 98.79148407802805, 98.80384030880471, 98.8161024831791, 98.82825920680233, 98.84036191384399, 98.85235865983353, 98.86430087515521, 98.8761957524363, 98.88798296634795, 98.8996889631474, 98.91133845459055, 98.92294835873409, 98.93440141415735, 98.94582311052436, 98.95706376543781, 98.96819129900472, 98.97924530777586, 98.99028838329114, 99.00129426354096, 99.01219174685416, 99.02302405358522, 99.03378362351845, 99.04448406057863, 99.05510455700885, 99.06569745700877, 99.0762024392913, 99.08654449487925, 99.09676951807991, 99.10697410272942, 99.11705867923197, 99.12708514991705, 99.13704492597088, 99.14698221932625, 99.15679471658491, 99.16655423069946, 99.17623734991669, 99.18578979172918, 99.19524427549271, 99.20462409754326, 99.2139963715142, 99.22324567701148, 99.23240442188109, 99.24154409868737, 99.25061151743894, 99.25961903136107, 99.26855607898422, 99.27747167501, 99.2862978140153, 99.29503060553213, 99.30366156491633, 99.31221910421482, 99.32073487930793, 99.32919508634231, 99.33752636832634, 99.34582416549006, 99.35407403566548, 99.36226518707612, 99.37037422402322, 99.37846453894105, 99.38642540276417, 99.39437223530047, 99.40223484778369, 99.41004096143021, 99.41778348366172, 99.42544250839406, 99.43302290004043, 99.44048386442144, 99.44786844066273, 99.45522535320862, 99.46250691479477, 99.46977831631683, 99.47698498748377, 99.48412662777496, 99.4912072063956, 99.49817237222884, 99.50509687475785, 99.51192683687577, 99.51872067621827, 99.52542653576259, 99.53204998108396, 99.53857424362636, 99.5449944929675, 99.55136553249754, 99.55771089095732, 99.56391416694095, 99.57004282583387, 99.57607472825255, 99.58206755674023, 99.58800436101775, 99.59387735147548, 99.59973941997235, 99.60547804147458, 99.61115058121506, 99.61678796273145, 99.62234961180243, 99.62783974069511, 99.63331362227437, 99.63876092245374, 99.64409393756125, 99.64936949742032, 99.65462426624693, 99.65984408998251, 99.66502929828424, 99.67013078699999, 99.67516889093866, 99.6801444336056, 99.68505117208038, 99.68992125447619, 99.6947154714379, 99.69943629449239, 99.70410236386732, 99.7087466252953, 99.71330678456538, 99.71779772709093, 99.72216907485961, 99.72646172837092, 99.73072262870046, 99.73496119003639, 99.73917861382239, 99.74335708729018, 99.74749579081296, 99.75158040897468, 99.75560909361606, 99.7594679678901, 99.76329316761857, 99.7671073570228, 99.77089574077833, 99.77462812250742, 99.77833554702634, 99.78199456418305, 99.78557105235308, 99.78910684765111, 99.79263215799915, 99.79611915776127, 99.7995742139968, 99.80301257108003, 99.80635282704904, 99.80965274502034, 99.81287259286879, 99.81606652815412, 99.81923060914565, 99.82233191500174, 99.82537283809616, 99.8283884405316, 99.83137906273954, 99.83430034765958, 99.83718699436793, 99.84003883947435, 99.8428453465662, 99.845636086627, 99.84838781876273, 99.85108235152704, 99.85365961582318, 99.8561888221768, 99.8587051192801, 99.86118794525038, 99.86365670159562, 99.86609234796089, 99.86852376026137, 99.87094866196631, 99.8733212435031, 99.87565637769599, 99.87797808590778, 99.88022992645604, 99.88246644879239, 99.88467829362835, 99.88682153218777, 99.88895107766622, 99.89105781483626, 99.89314344136588, 99.89518115229056, 99.89719012609692, 99.89917657540687, 99.90113902802977, 99.90309049583145, 99.90498645833087, 99.90683140664098, 99.90865006745919, 99.9104603164009, 99.91225604952527, 99.91401489173124, 99.91575588715611, 99.91739172316846, 99.91900903270053, 99.92061986969284, 99.92221026361482, 99.92376417411762, 99.9252847684116, 99.92680147239211, 99.92829942382481, 99.92977527092782, 99.93123309939281, 99.93266856659626, 99.9340862743334, 99.93548248874853, 99.9368614607783, 99.93822891801015, 99.93956223147319, 99.94087262586498, 99.94212749902941, 99.94336563446146, 99.9445841626974, 99.94578431723785, 99.94697557294953, 99.94815323466055, 99.94932630909952, 99.95046419024823, 99.95159587507236, 99.95272051132434, 99.9538207722528, 99.95491447502536, 99.95597148232595, 99.95702532274315, 99.95804852577088, 99.95905071748506, 99.96000820396293, 99.96094545225084, 99.96187148679658, 99.9627937123409, 99.96368087774256, 99.96456185765292, 99.96542108696596, 99.9662371055002, 99.96703409677355, 99.96782081590965, 99.96859420974806, 99.96935859856889, 99.97011635192477, 99.97086954640028, 99.97160640737553, 99.97233332825525, 99.97304819462157, 99.97374435710746, 99.9744324688394, 99.97510400514399, 99.97576958674011, 99.97642338791242, 99.97707039930177, 99.97768438963936, 99.97827712862774, 99.97884985219275, 99.97941757658268, 99.97997307466991, 99.98050801264141, 99.9810350856299, 99.9815533409017, 99.9820572632686, 99.9825568166921, 99.98305008580677, 99.98354017344215, 99.98402123774925, 99.98449083922857, 99.9849531680658, 99.98540862663086, 99.98582845509361, 99.98624694491848, 99.98664821779121, 99.98704837334988, 99.98744288666295, 99.98782286207143, 99.98820094755285, 99.98853216533888, 99.98885595302845, 99.98917721179977, 99.98949473108264, 99.98980668902652, 99.99011490539446, 99.9904174872144, 99.99071870138432, 99.99101577171857, 99.99131136509538, 99.99160382347857, 99.99188420044094, 99.99214704598705, 99.99240203957916, 99.99263820995785, 99.99286975682435, 99.99309605317818, 99.99332052794396, 99.99354129707251, 99.9937564125079, 99.99397107635086, 99.99418128030302, 99.99438545738646, 99.99457337227729, 99.99475987854855, 99.99494509838878, 99.99512954430163, 99.99530958133451, 99.9954850144011, 99.99564685808012, 99.99580739879097, 99.99595774604616, 99.99610385182422, 99.99624518208316, 99.99638401694983, 99.99651583737958, 99.99664616131747, 99.99677462592786, 99.99689930981614, 99.99701123014066, 99.99711907075026, 99.99722386568598, 99.99732802394746, 99.99743159875683, 99.99752972118775, 99.997626361699, 99.99771981096998, 99.99781138552571, 99.9979023640495, 99.99799226994921, 99.99807980863777, 99.99816312321674, 99.99824073634873, 99.99831523285076, 99.99838741685141, 99.99845408023916, 99.9985200532257, 99.99858374392095, 99.99864629998264, 99.99870883776961, 99.99876793034491, 99.99882621895405, 99.99888290727041, 99.99893900380516, 99.99899182532609, 99.99904405010982, 99.99909179824387, 99.9991389647981, 99.99918557842855, 99.99922880596887, 99.99927084965675, 99.99931149706964, 99.99934988584135, 99.99938609884298, 99.99942176503508, 99.99945299669011, 99.99948267976976, 99.99951052127747, 99.99953778935289, 99.99956353784931, 99.99958909280299, 99.99961322161217, 99.99963679218712, 99.99965978627482, 99.99968232149733, 99.99970382104661, 99.99972407466633, 99.99974421866109, 99.99976383548865, 99.99978150952388, 99.99979863239395, 99.9998137317399, 99.99982870356861, 99.99984236369187, 99.99985589415135, 99.99986869953518, 99.99987940450735, 99.99988885347132, 99.99989763738984, 99.99990596389475, 99.99991413199677, 99.99992098087226, 99.99992770456, 99.99993412561723, 99.99994008450456, 99.99994562476354, 99.99995028594378, 99.9999548794822, 99.99995894470878, 99.99996288054915, 99.99996648510545, 99.9999700544871, 99.99997329470388, 99.99997638231692, 99.99997938714769, 99.99998227786394, 99.99998468036948, 99.99998656503193, 99.99998833761123, 99.99999000060134, 99.99999162107582, 99.99999273609028, 99.99999376677113, 99.99999477661306, 99.99999564108428, 99.99999643688462, 99.9999971285218, 99.99999781704565, 99.99999836026268, 99.99999885684886, 99.99999922667102, 99.99999952870562, 99.9999997227134, 99.99999980945177, 99.99999988027068, 99.99999994949681, 99.99999997484746, 99.99999999846939, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999, 99.99999999999999], \"name\": \"cumulative explained variance\"}], {\"yaxis\": {\"title\": \"explained variance in percent\"}, \"title\": \"Cumulative Explained variance by different principal components 1 - 784\"}, {\"showLink\": true, \"linkText\": \"Export to plot.ly\"})});</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "basis_vecs = my_PCA()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above is the cumulative explained variance by principal components 1 - 784. The x-label is the principal components 1 - 784. Kindly mouse-over the plot to explore the PC and the cumulative explained variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### LOOCV and testing analysis were performed using 99%, 95%, 90%, 85%, and 75% variance explained, and their results are presented below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 331)"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_PCA = np.dot(train, basis_vecs[0][:,0:331])\n",
    "train_PCA.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 331)"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_PCA = np.dot(test, basis_vecs[0][:,0:331])\n",
    "test_PCA.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LOOCV and testing analysis having reduced the dimension of the dataset to 331 (99% Variance Explained):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAHHCAYAAAC2rPKaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ae212bc550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best value of K is 1 with an error of 2.5867%\n",
      "\n",
      "K = 1 will be used for the testing set:\n",
      "Testing Confusion Matrix: Actual vs. Prediction\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>973</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1129</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>994</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>14</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>968</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>941</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "      <td>861</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>944</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>990</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>14</td>\n",
       "      <td>5</td>\n",
       "      <td>12</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>922</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>966</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1    2    3    4    5    6    7    8    9\n",
       "0  973     1    1    0    0    1    3    1    0    0\n",
       "1    0  1129    3    0    1    1    1    0    0    0\n",
       "2    7     6  994    5    1    0    2   14    3    0\n",
       "3    1     1    2  968    1   19    0    7    7    4\n",
       "4    0     7    0    0  941    0    4    5    2   23\n",
       "5    1     1    0   11    2  861    6    1    5    4\n",
       "6    4     2    0    0    3    5  944    0    0    0\n",
       "7    0    15    6    2    5    0    0  990    0   10\n",
       "8    5     1    3   14    5   12    3    4  922    5\n",
       "9    2     5    1    6   10    5    1   12    1  966"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>digit</th>\n",
       "      <th>error per digit in %</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.7143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.5286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3.6822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>4.1584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>4.1752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>3.4753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1.4614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>3.6965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>5.3388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>4.2616</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   digit  error per digit in %\n",
       "0      0                0.7143\n",
       "1      1                0.5286\n",
       "2      2                3.6822\n",
       "3      3                4.1584\n",
       "4      4                4.1752\n",
       "5      5                3.4753\n",
       "6      6                1.4614\n",
       "7      7                3.6965\n",
       "8      8                5.3388\n",
       "9      9                4.2616"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The overall testing error is 3.12% for k = 1.\n"
     ]
    }
   ],
   "source": [
    "result_pca = knn_loocv_method(train_PCA, train_label, test_PCA, test_label, k_list=range(1, 21))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 155)"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_PCA_low = np.dot(train, basis_vecs[0][:,0:155])\n",
    "train_PCA_low.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 155)"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_PCA_low = np.dot(test, basis_vecs[0][:,0:155])\n",
    "test_PCA_low.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LOOCV and testing analysis having reduced the dimension of the dataset to 155  (95% Variance Explained): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAHHCAYAAAC2rPKaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3XlYlOX+P/D3jOwgIC6IioC472VaZEkKSqamaYmVgqil\nHteOedL6AjFTaWodLU0tDc0l18xMjMWt4Jia5oqamgsJQoIsIrLN/fvD30yOgMzAzDzDzPt1XXOd\nwzP3PM9nRnLe3tsjE0IIEBEREVkgudQFEBERERkLgw4RERFZLAYdIiIislgMOkRERGSxGHSIiIjI\nYjHoEBERkcVi0CEiIiKLxaBDREREFotBh4iIiCwWgw5ZlQMHDkAmk+HAgQNSl6Jl3bp1aN++PWxt\nbeHu7i51OQZlrp85EVkHBh2yCGvWrIFMJtM8HBwc0LZtW0ydOhWZmZkGuUZcXBzef/99g5zrQefP\nn8fYsWPh7++Pr776Cl9++WWVbd9//33IZDLcunVL63haWhr8/f3h4eGB48ePG7xGsi4fffQRvv/+\ne6nLIDIIG6kLIDIkhUIBPz8/3Lt3D8nJyVi+fDni4uJw5swZODk51erccXFxWLZsmcHDzoEDB6BS\nqbBkyRK0bt1a79ffuHEDffv2RU5ODpKSkvD4448btD6yPh999BFefvllDBs2TOpSiGqNQYcsysCB\nA/HEE08AACZMmICGDRvi008/xc6dO/Hqq69KXF3lsrKyAKBGQ1bp6eno27cvsrOzkZiYiB49ehi6\nPCKjUalUKCkpgYODQ4XnysrKoFKpYGdnV+PzG+IcVPdx6IosWr9+/QAAV65ceWS7rVu3okePHnB0\ndESjRo0wevRo3LhxQ/P82LFjsWzZMgDQGiKrzhdffIFOnTrB3t4ezZo1w5QpU5Cbm6t53tfXF9HR\n0QCAxo0bQyaT6dxjlJGRgb59+yIrKwsJCQmagFeVbdu2QSaT4eDBgxWeW7lyJWQyGc6cOQMAuHnz\nJiIiItCiRQvY29vDy8sLQ4cOxdWrV3WqTReHDx/G888/Dzc3Nzg5OSEwMBApKSlaba5du4Z//etf\naNeuHRwdHdGwYUO88sorWnX89ttvkMlkWLt2bYVrxMfHQyaT4ccff9Qcu3HjBsaNGwdPT0/Y29uj\nU6dO+Prrr3Wu+88//8Qrr7wCDw8PODk54amnnsLu3bu12qjnJW3ZsgUffvghWrRoAQcHBwQFBeHS\npUs1+iweZd++fXj22Wfh7OwMd3d3DB06FOfOndNqM3bsWPj6+lZ4rXo4VE0mk6GwsBBr167V/J6P\nHTv2kdcvLi5GdHQ0WrduDXt7e3h7e+M///kPiouLtdrJZDJMnToVGzZs0Px38dNPP+Hq1auQyWRY\ntGgRFi9eDH9/f9jb2yM1NRXA/X8MjB8/Hp6ennBwcEC3bt0q/HlXdw6yXuzRIYt2+fJlAEDDhg2r\nbLNmzRpERESgZ8+emDdvHjIzM7FkyRKkpKTg999/h7u7OyZOnIj09HQkJiZi3bp1Ol37/fffR0xM\nDIKDgzF58mRcuHABy5cvx9GjR5GSkgJbW1ssXrwY33zzDXbs2IHly5fDxcUFXbt2rfbcmZmZePnl\nl3Hz5k0kJCSgZ8+e1b5m0KBBcHFxwZYtWxAYGKj13ObNm9GpUyd07twZADBixAicPXsW06ZNg6+v\nL7KyspCYmIjr169X+mWpr3379mHgwIHo0aMHoqOjIZfLERsbi379+uGXX35Br169AABHjx7F//73\nP4waNQotWrTA1atXsXz5cjz33HNITU2Fk5MTnnjiCbRq1QpbtmxBeHh4hffVoEEDhISEaD63p556\nSvOF27hxY+zZswfjx49Hfn4+Zs6c+ci6MzMz8fTTT+Pu3buYPn06GjZsiLVr1+LFF1/Etm3b8NJL\nL2m1nz9/PuRyOd5++23k5eVhwYIFeP3113H48GG9P4uqJCUlYeDAgWjVqhXef/99FBUV4fPPP0fv\n3r1x/Phxvf+81q1bhwkTJqBXr1548803AQD+/v5VtlepVHjxxReRnJyMN998Ex06dMDp06fx3//+\nF3/88UeFuT779u3Dli1bMHXqVDRq1EirvtjYWNy7dw9vvvkm7O3t4eHhgaKiIjz33HO4dOkSpk6d\nCj8/P2zduhVjx45Fbm4uZsyYoXX+ys5BVk4QWYDY2FgBQCQlJYm///5bpKWliU2bNomGDRsKR0dH\n8ddffwkhhNi/f78AIPbv3y+EEKKkpEQ0adJEdO7cWRQVFWnO9+OPPwoAIioqSnNsypQpQtf/ZLKy\nsoSdnZ0YMGCAKC8v1xxfunSpACC+/vprzbHo6GgBQPz999/Vnlfd1sfHR7i6uopDhw7pVI/aq6++\nKpo0aSLKyso0xzIyMoRcLhcKhUIIIcTt27cFALFw4UK9zl2Vhz9zlUol2rRpI0JCQoRKpdK0u3v3\nrvDz8xP9+/fXOvawQ4cOCQDim2++0RybO3eusLW1FTk5OZpjxcXFwt3dXYwbN05zbPz48cLLy0vc\nunVL65yjRo0Sbm5ulV7vQTNnzhQAxC+//KI5VlBQIPz8/ISvr6/mz1r9njt06CCKi4s1bZcsWSIA\niNOnT+v9WVSle/fuokmTJiI7O1tz7OTJk0Iul4uwsDDNsfDwcOHj41Ph9erfqQc5OzuL8PDwaq8t\nhBDr1q0Tcrlc6zMRQogVK1YIACIlJUVzDICQy+Xi7NmzWm2vXLkiAAhXV1eRlZWl9dzixYsFALF+\n/XrNsZKSEhEQECBcXFxEfn5+tecg68ahK7IowcHBaNy4Mby9vTFq1Ci4uLhgx44daN68eaXtf/vt\nN2RlZeFf//qX1jyBQYMGoX379hWGJHSVlJSEkpISzJw5E3L5P/+ZvfHGG3B1da3xedUyMzPh4uIC\nLy8vvV4XGhqKrKwsraXe27Ztg0qlQmhoKADA0dERdnZ2OHDgAG7fvl2rOitz4sQJXLx4Ea+99hqy\ns7Nx69Yt3Lp1C4WFhQgKCsLPP/8MlUqlqUWttLQU2dnZaN26Ndzd3bVWl4WGhqK0tBTfffed5lhC\nQgJyc3M170sIge3bt2PIkCEQQmiue+vWLYSEhCAvL6/aFWtxcXHo1asXnnnmGc0xFxcXvPnmm7h6\n9WqFYZKIiAit+SHPPvssgPvDX/p+FpXJyMjAiRMnMHbsWK2ei65du6J///6Ii4t75PsxhK1bt6JD\nhw5o37691meqHjbev3+/VvvAwEB07Nix0nONGDECjRs31joWFxeHpk2bas2xs7W1xfTp03Hnzp0K\nQ7GVnYOsG4euyKIsW7YMbdu2hY2NDTw9PdGuXTutoPGwa9euAQDatWtX4bn27dsjOTm5RnVUdV47\nOzu0atVK83xNrV+/HqNHj0b//v2RnJyMJk2a6PQ69TyQzZs3IygoCMD94Z3u3bujbdu2AAB7e3t8\n/PHHmDVrFjw9PfHUU09h8ODBCAsLQ9OmTWtVNwBcvHgRACoMMz0oLy8PDRo0QFFREebNm4fY2Fjc\nuHEDQgitNmrdunVD+/btsXnzZowfP17zvho1aqT5wv3777+Rm5uLL7/8ssol/OqJ4Tdv3tQ67ubm\nBkdHR1y7dg1PPvlkhdd16NABwP0/d/XwHwC0bNlSq12DBg0AQBMgdf0snJ2dkZOTo3W8cePGj/z9\n7dChA+Lj41FYWAhnZ+cqz19bFy9exLlz56oMF+rPVM3Pz6/Kc1X23LVr19CmTZsK/x0/+Jnren6y\nTgw6ZFF69epV7aRcSxAYGIgtW7Zg+PDhCAkJwYEDB+Dm5lbt6+zt7TFs2DDs2LEDX3zxBTIzM5GS\nkoKPPvpIq93MmTMxZMgQfP/994iPj0dkZCTmzZuHffv24bHHHqtV7eoeioULF6J79+6VtnFxcQEA\nTJs2DbGxsZg5cyYCAgLg5uYGmUyGUaNGVejpCA0NxYcffohbt26hfv36+OGHH/Dqq6/CxsZG67qj\nR4+uMlio50c93FMWGxtb7YTcytSrV6/S4+rAputnkZKSgr59+2odr26C/cOqmjxfXl6u13keplKp\n0KVLF3z66aeVPu/t7a3184O9dA971HO6MsQ5yLIw6JBV8/HxAQBcuHBB8y9/tQsXLmieB6r+oqju\nvK1atdIcLykpwZUrVxAcHFybsgEAQ4YMwddff43w8HAMHjwYCQkJOv0lHxoairVr12Lv3r04d+4c\nhBCa4Z0H+fv7Y9asWZg1axYuXryI7t2745NPPsH69etrVbd6Yqurq2u1n8O2bdsQHh6OTz75RHPs\n3r17WivXHnxfMTEx2L59Ozw9PZGfn49Ro0Zpnm/cuDHq16+P8vLyaq+bmJio9XOnTp0A3P9zvXDh\nQoX258+f1zyvD10/i27dulWoqWnTprC3tweAKmtq1KiRpjenQYMGlX5ulfUu6vO77u/vj5MnTyIo\nKEiv1+nKx8cHp06dgkql0urVqelnTtaHc3TIqj3xxBNo0qQJVqxYobUUds+ePTh37hwGDRqkOab+\nwqjsy+JhwcHBsLOzw2effaY13LJ69Wrk5eVpnbc2xowZg8WLFyM5ORkjRoxAaWmpTrV5eHhg8+bN\n2Lx5M3r16qXV3X/37l3cu3dP6zX+/v6oX7++1meUkZGB8+fP63TNB/Xo0QP+/v5YtGgR7ty5U+H5\nv//+W/P/69Wrp/X5AcDnn39eaS9Ehw4d0KVLF8378vLyQp8+fbTONWLECGzfvl2zjL6q6wYHB2s9\n1D08L7zwAo4cOYJDhw5p2hYWFuLLL7+Er69vlXNPqqLrZ9GgQYMKNTk4OMDLywvdu3fH2rVrtX4v\nz5w5g4SEBLzwwguaY/7+/sjLy8OpU6c0xzIyMrBjx44K13V2dtbp9xwARo4ciRs3buCrr76q8FxR\nUREKCwt1Ok9VXnjhBdy8eRObN2/WHCsrK8Pnn38OFxeXCisIiR7GHh2yara2tvj4448RERGBwMBA\nvPrqq5rl5b6+vnjrrbc0bdWb8U2fPh0hISGoV6+eVo/Bgxo3boy5c+ciJiYGzz//PF588UVcuHAB\nX3zxBXr27InRo0cb7D1Mnz4dOTk5iImJQVhYGDZs2PDIeUm2trYYPnw4Nm3ahMLCQixatEjr+T/+\n+ANBQUEYOXIkOnbsCBsbG+zYsQOZmZla73fu3LlYu3Ytrly5otcSZrlcjlWrVmHgwIHo1KkTIiIi\n0Lx5c9y4cQP79++Hq6srdu3aBQAYPHgw1q1bBzc3N3Ts2BGHDh1CUlJSldsFhIaGIioqCg4ODhg/\nfnyFz2H+/PnYv38/nnzySbzxxhvo2LEjcnJycPz4cSQlJVWYB/OwOXPm4Ntvv8XAgQMxffp0eHh4\naD6D7du3P/Jzr+1nUZWFCxdi4MCBCAgIwPjx4zXLy93c3LT2ZBo1ahTeeecdvPTSS5g+fTru3r2L\n5cuXo23bthUmYffo0QNJSUn49NNP0axZM/j5+VU6Nwm4H7a3bNmCSZMmYf/+/ejduzfKy8tx/vx5\nbNmyBfHx8bUaTn7zzTexcuVKjB07FseOHYOvry+2bduGlJQULF68GPXr16/xuclKSLjii8hg1MvL\njx49+sh2Dy91Vtu8ebN47LHHhL29vfDw8BCvv/66Zkm6WllZmZg2bZpo3LixkMlkOi01X7p0qWjf\nvr2wtbUVnp6eYvLkyeL27dtabWqyvLyyttOmTRMAxKRJk6o9T2JiogAgZDKZSEtL03ru1q1bYsqU\nKaJ9+/bC2dlZuLm5iSeffFJs2bJFq114eLgAIK5cufLIa1X1mf/+++9i+PDhomHDhsLe3l74+PiI\nkSNHir1792ra3L59W0RERIhGjRoJFxcXERISIs6fPy98fHwqXf588eJFAUAAEMnJyZXWk5mZKaZM\nmSK8vb2Fra2taNq0qQgKChJffvnlI9+H2uXLl8XLL78s3N3dhYODg+jVq5f48ccfK33PW7du1Tqu\nXgIdGxur92fxKElJSaJ3797C0dFRuLq6iiFDhojU1NQK7RISEkTnzp2FnZ2daNeunVi/fn2ly8vP\nnz8v+vTpIxwdHQWAapeal5SUiI8//lh06tRJ2NvbiwYNGogePXqImJgYkZeXp2kHQEyZMqXC69Wf\nS1VbGmRmZmp+D+zs7ESXLl0qfIbVnYOsl0yIh/qFiYiIiCwE5+gQERGRxWLQISIiIovFoENEREQW\ni0GHiIiILBaDDhEREVksBh0iIiKyWFa3YaBKpUJ6ejrq169vlO3KiYiIyPCEECgoKECzZs302pzT\n6oJOenp6hZvMERERUd2QlpaGFi1a6Nze6oKOervwtLQ0uLq6SlwNERER6SI/Px/e3t563/bD6oKO\nerjK1dWVQYeIiKiO0XfaCScjExERkcVi0CEiIiKLxaBDREREFkvSoLN8+XJ07dpVM18mICAAe/bs\n0em1KSkpsLGxQffu3Y1cJREREdVVkgadFi1aYP78+Th27Bh+++039OvXD0OHDsXZs2cf+brc3FyE\nhYUhKCjIRJUSERFRXSQTQgipi3iQh4cHFi5ciPHjx1fZZtSoUWjTpg3q1auH77//HidOnND5/Pn5\n+XBzc0NeXh5XXREREdURNf3+Nps5OuXl5di0aRMKCwsREBBQZbvY2Fj8+eefiI6O1um8xcXFyM/P\n13oQERGRdZB8H53Tp08jICAA9+7dg4uLC3bs2IGOHTtW2vbixYuYM2cOfvnlF9jY6Fb6vHnzEBMT\nY8iSiYiIqI6QvEenXbt2OHHiBA4fPozJkycjPDwcqampFdqVl5fjtddeQ0xMDNq2bavz+efOnYu8\nvDzNIy0tzZDlExER0QOUSiXkcjmUSqXUpQAwwzk6wcHB8Pf3x8qVK7WO5+bmokGDBqhXr57mmEql\nghAC9erVQ0JCAvr161ft+TlHh4iIyDiUSiWioqI0PysUCkRGRhrk3DX9/pZ86OphKpUKxcXFFY67\nurri9OnTWse++OIL7Nu3D9u2bYOfn5+pSiQiIqKHPBxyAGh+NlTYqQlJg87cuXMxcOBAtGzZEgUF\nBdi4cSMOHDiA+Ph4zfM3btzAN998A7lcjs6dO2u9vkmTJnBwcKhwnIiIiEynspCjJnXYkTToZGVl\nISwsDBkZGXBzc0PXrl0RHx+P/v37AwAyMjJw/fp1KUskIiKiR3hUyFGTMuyY3RwdY+McHSIiIsPQ\nJeQ8qDZzdmr6/c2gQ0RERDUil8uhT4yQyWRQqVQ1ulad3zCQiIiI6hZ996mTYl87Bh0iIiKqkf/8\n5z/o0qWLTm0NudRcHww6REREpLfs7GwEBwfj9OnTkMsfHSekCjkAgw4RERHp6dKlSwgICEBycjJc\nXV2RkJAAhUJRaVspQw5ghhsGEhERkflKSUnB0KFDkZ2dDR8fH+zevRudOnVCUFAQABhtZ+SaYo8O\nERER6WTz5s0ICgpCdnY2evbsiV9//RWdOnXSPB8ZGQmFQgGZTGYWIQfg8nKpyyEiIjJ7QgjMnz8f\n7777LgBg2LBh2LBhA5ycnExWA5eXExERkcGVlpbijTfe0ISct956C9u2bTNpyKkNztEhIiKiSuXl\n5eHll19GUlIS5HI5PvvsM0yZMkXqsvTCoENEREQVXLt2DYMGDcLZs2fh7OyMTZs2YfDgwVKXpTcG\nHSIiItJy7NgxDB48GDdv3oSXlxd+/PFHPP7441KXVSOco0NEREQaO3fuRJ8+fXDz5k106dIFhw8f\nrrMhB2DQISIiov9vyZIleOmll3D37l2EhIQgOTkZ3t7eUpdVKww6REREVkSpVEIul0OpVGqOlZeX\nY/r06Zg5cyaEEHjzzTexa9cui9iGhXN0iIiIrIRSqdTsXKz+37feeguvvfYadu3aBQBYsGAB3n77\nbchkMsnqNCRuGEhERGQFHgw5D/Ly8kJGRgYcHBywbt06vPzyyxJUV72afn+zR4eIiMjCVRVyACAj\nIwNOTk5ISkpCQECAiSszPs7RISIismCPCjlqd+/eRVJSkokqMi0GHSIiIgulS8hRi4qK0pqgbCk4\nR4eIiMhCyeVy6PM1L5PJoFKpjFhRzfGmnkRERKRl8uTJerWPiYkxUiXSYdAhIiKyIEIIJCYmIiQk\nBF988YXOr1MoFIiMjDRiZdLgqisiIiILUFpaii1btmDRokU4ceIEgPtDV6+88grc3d2xcuXKKl9r\nqSEHYNAhIiKq0woKCvDVV19h8eLFSEtLAwA4OTlhwoQJmDlzJvz8/AAAzZs3r3RisiWHHIBDV0RE\nRGansts0PCw9PR1z5syBt7c3Zs2ahbS0NHh6euKDDz5AWloalixZogk5ABAZGQmFQqF1DksPOQB7\ndIiIiMxKZbdpeDCMnD17FosWLcKGDRtQWloKAGjXrh3efvttjB49Gg4ODlWeW32e6OhoxMTEWHzI\nAbi8XOpyiIiINKra9yYmJgbPPvssFi5ciD179miOP/PMM5g9ezYGDx4MudyyB2lq+v3NoENERGQG\ndN3cTyaTYfjw4Xj77bfx1FNPmaAy88B7XREREdVRuoacnj17YuPGjWjdurUJqrIMlt3PRUREZOb0\nuU3D0aNH8e233xq5IsvCoSsiIiIJWdJtGoyJt4AgIiKqg/S97YIl3qbBmBh0iIiIJDRz5kyd59xY\nw743hsagQ0REJJG//voLzzzzDC5dugQbm0evD2LIqRkGHSIiIgmcOHECTz75JE6dOgVPT0/873//\nq7BzsRpDTs1xeTkREZGJxcXFYeTIkSgsLETHjh2xe/du+Pr6omfPngCgtQqLIad22KNDRERkQl98\n8QWGDBmCwsJCBAUFISUlBb6+vprn1fekkslkDDkGwOXlREREJqBSqTB79mx8+umnAICIiAisWLEC\ndnZ2EldWN3BnZCIiIjN19+5djB49Gjt27AAAfPDBB3j33Xchk8kkrszyMegQEREZUWZmJl588UUc\nOXIEdnZ2WLNmDV599VWpy7IaDDpERERGkpqaikGDBuHq1avw8PDAzp078cwzz0hdllXhZGQiIiIj\n2LdvH55++mlcvXoVrVu3xq+//sqQIwEGHSIiIgNbu3YtQkJCkJeXh969e+PQoUNo06aN1GVZJQYd\nIiIiAxFCICoqCmPHjkVZWRlGjRqFpKQkNGrUSOrSrBaDDhERkQEUFxdjzJgxUCqVAIB3330XGzZs\ngIODg8SVWTcGHSIiIj0plUrI5XJNqMnJycGAAQOwYcMG2NjYYPXq1fjwww8hl/NrVmpcdUVERKQH\npVKpuUVDVFQUsrOzsWfPHvzxxx9wdXXF9u3bERwcLHGVpMagQ0REpKMHQ47akiVLAAAtW7ZEXFwc\nOnXqJEVpVAX2qREREemgspDzoNDQUIYcM8SgQ0REVI3qQg4ALFy4UDNnh8wHgw4REdEj6BJy1KKi\nohh2zAzvXk5ERPQIcrkc+nxVymQyqFQqI1ZknWr6/c0eHSIiokeYM2eOXu1jYmKMVAnVBIMOERFR\nFfbu3Yt169bp3F6hUCAyMtKIFZG+GHSIiIgeUlRUhLfeegvBwcH466+/0Lp1a7zxxhuPfA1Djnni\nPjpEREQP+P333zF69GikpqYCACZNmoRFixbB2dkZ3t7elU5MZsgxX5L26Cxfvhxdu3aFq6srXF1d\nERAQgD179lTZ/rvvvkP//v3RuHFjTfv4+HgTVkxERJaqrKwMH330EXr16oXU1FQ0bdoUu3fvxvLl\ny+Hs7AwAiIyMhEKh0HodQ455kzTotGjRAvPnz8exY8fw22+/oV+/fhg6dCjOnj1bafuff/4Z/fv3\nR1xcHI4dO4a+fftiyJAh+P33301cORERWZLLly8jMDAQ7733HsrKyjB8+HCcPn0aL7zwQoW26rAj\nk8kYcuoAs1te7uHhgYULF2L8+PE6te/UqRNCQ0N13uOAy8uJiEhNCIFVq1bhrbfeQmFhIerXr4+l\nS5dizJgxkMlkUpdHD6jp97fZzNEpLy/H1q1bUVhYiICAAJ1eo1KpUFBQAA8PjyrbFBcXo7i4WPNz\nfn5+rWslIqK6LzMzExMmTMCPP/4IAAgMDMTatWvh4+MjcWVkSJKvujp9+jRcXFxgb2+PSZMmYceO\nHejYsaNOr120aBHu3LmDkSNHVtlm3rx5cHNz0zy8vb0NVToREdVR33//Pbp06YIff/wRdnZ2WLRo\nEfbt28eQY4EkDzrt2rXDiRMncPjwYUyePBnh4eGame6PsnHjRsTExGDLli1o0qRJle3mzp2LvLw8\nzSMtLc2Q5RMRkRlSKpWQy+UVbsdQUFCA8ePH46WXXsLff/+Nrl274rfffsOsWbMgl0v+lUhGYHZz\ndIKDg+Hv74+VK1dW2WbTpk0YN24ctm7dikGDBul1fs7RISKybA/fm0o9YTg5ORlhYWG4cuUKZDIZ\nZs+eDYVCAXt7ewmrJV3V+Tk6aiqVSmtOzcO+/fZbjBs3Dps2bdI75BARkWWr7AacUVFRSExMRHJy\nMoQQ8PX1xdq1a9GnTx+JqiRTkjTozJ07FwMHDkTLli1RUFCAjRs34sCBA5q9cebOnYsbN27gm2++\nAXB/uCo8PBxLlizBk08+iZs3bwIAHB0d4ebmJtn7ICIi6T3qLuO//PILACAiIgKLFy9mj74VkXRA\nMisrC2FhYWjXrh2CgoJw9OhRxMfHo3///gCAjIwMXL9+XdP+yy+/RFlZGaZMmQIvLy/NY8aMGVK9\nBSIiMgOPCjkP8vPzY8ixMmY3R8fYOEeHiMiy6Bpy1LjJX91U0+9vBh0iIqrT5HI59Pkqk8lkUKlU\nRqyIjKGm399cS0dERHXa+++/r1f7mJgY4xRCZolBh4iI6qyTJ08iMTFR5/YctrI+DDpERFTn5OXl\nYcaMGXj88ceRnJwMZ2dnzUKWqjDkWCcGHSIiqjOEEPjmm2/Qrl07fPbZZ1CpVHjllVdw7tw5JCQk\nQKFQVPo6hhzrZXYbBhIREVXm5MmTmDp1KpKTkwHcv4XQ0qVLERwcrGmjDjOV7YxM1ok9OkREZNZy\nc3MrDFN9/PHHOHXqlFbIUYuMjIRCoYBMJmPIIS4vJyIi8ySEwLp16zB79mxkZWUBAEaOHIlPPvkE\nLVq0kLjtpSYTAAAgAElEQVQ6MjUuLyciojqlqjuMA/eHqfr06YPw8HBkZWWhffv2SExMxObNmxly\nSC8MOkREZHLq3YyFEIiKitKEnaqGqU6ePFnpMBVRdTgZmYiITKqqO4yfOHECycnJHKYig2LQISIi\nk3nUfam+++47AED79u3x+eefsweHDIJDV0REZBK63nwzNDSUIYcMhkGHiIiMTp87jMfExFQ6QZmo\nJri8nIiIjI53GKfa4vJyIiIyW/reMZx3GCdDYdAhIiKji4yMxPTp03Vqy92MyZAYdIiIyOiuXr2q\nWVX1KAw5ZGgMOkREZFQZGRkIDg7GX3/9hQ4dOuCdd96ptB1DDhkD99EhIiKjuXXrFoKDg3H58mX4\n+fkhMTERzZs3h7OzM+8wTibBHh0iIjKKvLw8hISEIDU1Fc2bN8fevXvRvHlzALzDOJkOl5cTEZHB\nFRYWIiQkBCkpKWjcuDF+/vlntG/fXuqyqA7j8nIiIjILxcXFeOmll5CSkgJ3d3ckJCQw5JBkGHSI\niMhgSktLMWrUKCQmJsLZ2RlxcXHo3r271GWRFWPQISIig1CpVIiIiMD3338Pe3t7/PDDDwgICJC6\nLLJyDDpERFRrQgj861//woYNG2BjY4Nt27ahX79+UpdFxKBDRES1I4TA7NmzsXLlSsjlcqxfvx6D\nBw+WuiwiAAw6RERUS0qlEp988gkA4KuvvkJoaKjEFRH9g0GHiIhq7L///S+io6MBAIsXL8a4ceMk\nrohIG4MOERHVyFdffYV///vfAO736syYMUPiiogqYtAhIiK9bdy4ERMnTgQA/Oc//8F7770ncUVE\nlWPQISIivezcuRNhYWGalVbz58+HTCaTuiyiSjHoEBGRzpKSkjBy5EiUl5cjLCwMn3/+OUMOmTUG\nHSIiqpRSqYRcLodSqQQApKSkYOjQoSgpKcGIESOwevVqyOX8GiHzZiN1AUREZH6USiWioqIAAFFR\nUUhPT8fGjRtx9+5dPP/885qNAYnMHX9LiYhIy4MhR23FihUAgD59+mD79u2wt7eXojQivbHPkYiI\nNCoLOQ969tln4eTkZMKKiGqHQYeIiABUH3IA4MMPP9TM2SGqCxh0iIhIp5CjFhUVxbBDdYZMCCGk\nLsKU8vPz4ebmhry8PLi6ukpdDhGRWZDL5dDn60Amk0GlUhmxIiJtNf3+Zo8OEREhJibGqO2JpMKg\nQ0REiIyM1Ny3qjoKhQKRkZFGrojIMBh0iIgIV65cwfbt26ttx5BDdQ2DDhGRlbt06RICAwNx7do1\ntGnTBm+//Xal7RhyqC7ihoFERFbsjz/+QN++fZGeno727dtj37598PLygqurq9YqLIYcqqvYo0NE\nZKXOnz+PwMBApKeno2PHjjhw4AC8vLwA3J+zo1AoIJPJGHKoTuPyciIiK3T27Fn069cPWVlZ6NKl\nC/bu3YvGjRtLXRZRlbi8nIiIdHLq1Ck899xzyMrKQvfu3bFv3z6GHLJYDDpERFbkxIkT6NevH27d\nuoUePXpg7969aNSokdRlERkNgw4RkZU4duwY+vXrh+zsbPTq1QtJSUnw8PCQuiwio2LQISKyAkeO\nHEFQUBBu376NgIAAJCQkwN3dXeqyiIyOQYeIyMIdOnQI/fv3R15eHp555hnEx8fDzc1N6rKITIJB\nh4jIgiUnJ2PAgAHIz89HYGAg9uzZg/r160tdFpHJMOgQEVmogwcP4vnnn8edO3fQr18/7N69Gy4u\nLlKXRWRSDDpERBZo7969GDhwIAoLCzFgwAD8+OOPcHZ2lrosIpNj0CEisjAJCQkYPHgwioqKMHDg\nQOzcuROOjo5Sl0UkCQYdIqI6SqlUQi6XQ6lUao7FxcXhxRdfxL179zB48GDs2LEDDg4OElZJJC1J\ng87y5cvRtWtXuLq6wtXVFQEBAdizZ88jX3PgwAE8/vjjsLe3R+vWrbFmzRrTFEtEZEaUSiWioqIg\nhEBUVBSUSiV27dqFl156CcXFxRg2bBi2b98Oe3t7qUslkpSkdy9v0aIF5s+fjzZt2kAIgbVr12Lo\n0KH4/fff0alTpwrtr1y5gkGDBmHSpEnYsGED9u7diwkTJsDLywshISESvAMiItNTh5wHRUVFQS6X\nQ6VSYcSIEfj2229ha2srUYVE5sPsburp4eGBhQsXYvz48RWee+edd7B7926cOXNGc2zUqFHIzc3F\nTz/9pNP5eVNPIqrLKgs5D+rcuTOOHz/OkEMWp87f1LO8vBybNm1CYWEhAgICKm1z6NAhBAcHax0L\nCQnBoUOHqjxvcXEx8vPztR5ERHVRdSEHAM6cOYP58+ebqCIi8yd50Dl9+jRcXFxgb2+PSZMmYceO\nHejYsWOlbW/evAlPT0+tY56ensjPz0dRUVGlr5k3bx7c3Nw0D29vb4O/ByIiY9Ml5Kip5+wQkRkE\nnXbt2uHEiRM4fPgwJk+ejPDwcKSmphrs/HPnzkVeXp7mkZaWZrBzExGZSnR0tFHbE1kqSScjA4Cd\nnR1at24NAOjRoweOHj2KJUuWYOXKlRXaNm3aFJmZmVrHMjMz4erqWuUeEfb29lx1QER1VlZWFr77\n7jv4+vriypUrOr8uJibGiFUR1R2S9+g8TKVSobi4uNLnAgICsHfvXq1jiYmJVc7pISKSWmV73VTn\n1q1b+OqrrxAcHAwvLy9MnjxZr5CjUCgQGRlZk3KJLI+Q0Jw5c8TBgwfFlStXxKlTp8ScOXOETCYT\nCQkJmufHjBmjaf/nn38KJycnMXv2bHHu3DmxbNkyUa9ePfHTTz/pfM28vDwBQOTl5Rn8/RARPUih\nUAgAmodCoaiybXZ2tli1apUYMGCAqFevntbrnnjiCbFgwQJx5cqVCud8+PGoaxDVZTX9/pY06Iwb\nN074+PgIOzs70bhxYxEUFKQJOUIIER4eLgIDA7Ves3//ftG9e3dhZ2cnWrVqJWJjY/W6JoMOEZlC\nVYHkwSCSk5MjYmNjxfPPPy9sbGy02j3++ONi/vz54vLlyzU6N5Glqen3t9nto2Ns3EeHiIytuhVS\nw4cPR3FxMRISElBaWqo53q1bN4wcORIjR47UzF3U9RocriJLV9Pvb8knIxMRWRJdloF/9913mv/f\npUsXjBw5Eq+88gratWun83XUoSY6OhoxMTEMOURVYI8OEZGB6LPXDQBMmzYNn332mRErIrIcNf3+\nZtAhIjIQuVwOff5KlclkUKlURqyIyHLU+VtAkG5qslSViExD371ruNcNkfEx6NQh6m5xIQS3eCcy\nQ5GRkXjvvfd0asvJw0SmwaBTR1Q29s+wQ2Re7t27h5SUlGrbMeQQmQ6DTh3wqAmODDtE5qGsrAyh\noaE4cOAA6tevj0mTJlXajiGHyLT0CjqlpaWwsbHBmTNnjFUPPUSXVRwMO0TSUqlUmDBhAn744QfY\n29tj165dWL58ORQKhVY7hhwi09Mr6Nja2qJly5YoLy83Vj30AH2WqjLsEElDCIFZs2Zh7dq1qFev\nHrZu3YrAwEAA9+fsKBQKyGQyhhwiiei9vHz16tX47rvvsG7dOnh4eBirLqOpS8vLuVSVyPx98MEH\nmgDzzTffYMyYMRJXRGSZTLYz8tKlS3Hp0iU0a9YMPj4+cHZ21nr++PHj+p6SqhATE6PX5mNcqkpk\nWsuXL9eEnMWLFzPkEJkhvYPOsGHDjFEHVUL9F6guYYfd4kSm9e2332LKlCkA7v83OmPGDIkrIqLK\ncGfkOqC6uToMOUSmFRcXh6FDh6KsrAxTp07FZ599BplMJnVZRBbN5Df1PHbsGM6dOwcA6NSpEx57\n7LGanoqqERkZCZVKhffff7/Ccww5RKaVnJyMl19+GWVlZXjttdewZMkShhwiM6Z3j05WVhZGjRqF\nAwcOwN3dHQCQm5uLvn37YtOmTWjcuLFRCjWUutijAwDXr1+Hj4+P1jGGHCLTOnnyJAIDA5GXl4dB\ngwZhx44dsLW1lbosIqtgsntdTZs2DQUFBTh79ixycnKQk5ODM2fOID8/H9OnT9f3dKSjS5cuaf3c\nuXNnhhwiE7p06RJCQkKQl5eHZ555Blu2bGHIIaoD9B66+umnn5CUlIQOHTpojnXs2BHLli3DgAED\nDFoc/ePy5csAgHr16qG8vBwuLi4SV0RkPW7cuIH+/fsjMzMT3bp1w65du+Dk5CR1WUSkA717dFQq\nVaX/irG1teUeLkak7tHp1asXAODatWtSlkNkNXJychASEoKrV6+idevWiI+P1wzbE5H50zvo9OvX\nDzNmzEB6errm2I0bN/DWW28hKCjIoMXRP9RBJzg4GACQkZGBe/fuSVkSkcW7c+cOXnjhBZw9exbN\nmjVDYmIiPD09pS6LiPSgd9BZunQp8vPz4evrC39/f/j7+8PPzw/5+fn4/PPPjVEj4Z+hqyeffFLT\nZX79+nUpSyKyaMXFxXjppZdw+PBheHh4IDExEb6+vlKXRUR60nuOjre3N44fP46kpCScP38eANCh\nQwdNTwMZnhBC06PTpk0b+Pr6IjU1FdeuXUPbtm0lro7I8pSXl2P06NFISkqCs7Mz9uzZg44dO0pd\nFhHVgF5Bp7S0FM8//zxWrFiB/v37o3///saqix6QmZmJwsJCyOVy+Pr6aoLO1atXpS6NyOIIITBp\n0iRs27YNdnZ2+P777zVz44io7tH77uWnTp0yVi1UBXVvTsuWLWFnZ6fZT4dBh6yBUqmEXC6HUqk0\nyfnnzJmDVatWQS6X49tvv2VvNVEdp/ccndGjR2P16tXGqIWqoJ6f07p1awDQzBPgyiuydOrbnwgh\nEBUVZfCw8/D5BwwYgAULFgAAvvzySwwfPtyg1yMi09N7jk5ZWRm+/vprJCUloUePHhXuXv7pp58a\nrDi6T92j83DQYY8OWbLK7vGm/tkQm2VWdv7ExEQAwIIFCzB+/PhaX4OIpKd30Dlz5gwef/xxAMAf\nf/yh9Rzv92Ic6qDj7+8PABy6Iov3qBvZGiLsVHejXG7dQGQ59A46+/fvN0Yd9AhVDV2lp6ejpKQE\ndnZ2UpVGZHDVhRDgftgpLCzEv//9b73P/+mnn+Ljjz+u9vyAYXqOiEhaet3Us7S0FI6Ojjhx4gQ6\nd+5szLqMpi7e1NPDwwO3b9/G6dOn0blzZwgh4OTkhHv37uHSpUuanh6iuk6XkGNKvHEukfkwyU09\nbW1t0bJlS5SXl+tdINVMTk4Obt++DQBo1aoVgPtDhBy+IksUHR0tdQlazK0eItKf3quu3nvvPbz7\n7rvIyckxRj30EPX8nGbNmmndRJArr8gSxcTE6NVeoVBACKHzQ6FQGLUeIjI/es/RWbp0KS5duoRm\nzZrBx8enwqqr48ePG6w4qjg/R40rr8gSqYeJdBm+qsmwkrHPT0TmR++gM2zYMGPUQVV4eGm5GoMO\nWarIyEgkJCQgOTm5yja1CSG6hB2GHCLLoXfQ4Zi1aT28tFyNc3TIUqWkpCAlJaXK5w0RQh4Vdhhy\niCyLznN0jhw58shJyMXFxdiyZYtBiqJ/VNejwzk6ZEnu3LmD8PBwCCEQHh5eYU6NIUNIZGSkUc9P\nRGZC6Egul4vMzEzNz/Xr1xeXL1/W/Hzz5k0hl8t1PZ1k8vLyBACRl5cndSk68fT0FADEsWPHtI6n\np6cLAEIul4uSkhKJqiMyrMmTJwsAwtvbW+Tm5gohhFAoFEImkwmFQmGUaxr7/ERkGDX9/tZ5Hx25\nXI6bN2+iSZMmAID69evj5MmTmiXPmZmZ8PLygkqlMkogM5S6tI9OQUGBpsbc3Fy4ublpnlOpVHB0\ndERJSQn+/PNP+Pn5SVUmkUHEx8fj+eefBwAkJSUhKChI4oqIyJyYZB+d6vAWEIalXnHVqFEjrZAD\n3A+e6nk6HL6iuu727dsYN24cAGDatGkMOURkMAYNOmRYVS0tV+PKK7IU06ZNQ3p6Otq2bYv58+dL\nXQ4RWRC9Vl2lpqbi5s2bAAAhBM6fP487d+4AAG7dumX46qxcVROR1bjyiizB9u3bsWHDBsjlcqxd\nu1ZrY0wiotrSK+gEBQXhwSk9gwcPBnB/yEoIwaErA6tqabkaV15RXZeZmYmJEycCAObMmYOnnnpK\n4oqIyNLoHHSuXLlizDqoEtX16HDoiuoyIQTeeOMNZGdno1u3btyji4iMQuegox4mIdOpbo4Oh66o\nLluzZg127doFOzs7rFu3DnZ2dlKXREQWiJORzVRRURHS0tIAVD909ddff6GsrMxUpRHV2rVr1zBj\nxgwA9zfp69Kli8QVEZGlYtAxU+qhQldXVzRq1KjSNl5eXrC1tUVZWRnS09NNWR5RjalUKkRERKCg\noABPP/003n77balLIiILxqBjph4ctqpqkne9evXg7e0NgMNXVHcsXboU+/fvh5OTE9auXYt69epJ\nXRIRWTAGHTNV3URkNa68orrkwoULeOeddwAAixYtqvb3m4iotvS+e/mDbt26hcOHD6O8vBw9e/aE\nl5eXoeqyetUtLVfjyiuqK8rKyhAWFoZ79+5hwIABmDRpktQlEZEVqHHQ2b59O8aPH4+2bduitLQU\nFy5cwLJlyxAREWHI+qyWvj06DDpk7ubPn48jR47Azc0Nq1ev5r5bRGQSOg9dqXdAVouJicGRI0dw\n5MgR/P7779i6dSvee+89gxdorapbWq7G+11RXfD7778jJiYGwP05Oi1atJC4IiKyFjoHnR49emDn\nzp2an21sbJCVlaX5OTMzk/tgGEhpaammh4Y9OlTXFRcXIywsDGVlZRg+fDhef/11qUsiIiui89BV\nfHw8pkyZgjVr1mDZsmVYsmQJQkNDUV5ejrKyMsjlcqxZs8aIpVqPa9euoby8HI6OjtXOe1IHnevX\nr6O8vJwrWMjsREVF4cyZM2jSpAlWrFjBISsiMimdg46vry92796Nb7/9FoGBgZg+fTouXbqES5cu\noby8HO3bt4eDg4Mxa7Ua6mErf3//ar8UmjVrhnr16qG0tBQZGRkcEiCzkpKSgoULFwIAvvrqKzRu\n3FjiiojI2ui9vPzVV1/F0aNHcfLkSTz33HNQqVTo3r07Q44B6ToRGbg/hKjeS4fzdMic3LlzB+Hh\n4RBCYOzYsXjxxRelLomIrJBeQScuLg6ffPIJfvvtN6xatQoLFizA66+/jtmzZ6OoqMhYNVodXZeW\nq3GeDpmj2bNn4/Lly2jZsiUWL14sdTlEZKV0DjqzZs1CREQEjh49iokTJ0KpVCIwMBDHjx+Hg4MD\nHnvsMezZs8eYtVoNfXp0AN7ck8xPfHw8VqxYAQCIjY2Fm5ubxBURkbXSOeisWbMGcXFx2LRpE44e\nPYp169YBAOzs7KBUKvHdd9/ho48+Mlqh1kTXpeVq3B2ZzMnt27cxbtw4AMC0adPQr18/iSsiImum\nc9BxdnbW3GgyLS2twpycjh074pdffjFsdVaovLy8xkGHPTpkDqZNm4b09HS0bdsW8+fPl7ocIrJy\nOgedefPmISwsDM2aNUNgYCCUSmWtLz5v3jz07NkT9evXR5MmTTBs2DBcuHCh2tdt2LAB3bp1g5OT\nE7y8vDBu3DhkZ2fXuh5zcOPGDZSUlMDW1lYzybg6HLoiKSmVSsjlciiVSmzfvh0bNmyAXC7HN998\nAycnJ6nLIyIrp3PQef3115GWloadO3fi6tWrGDp0aK0vfvDgQUyZMgW//vorEhMTUVpaigEDBqCw\nsLDK16SkpCAsLAzjx4/H2bNnsXXrVhw5cgRvvPFGresxB+r5OX5+fjrvifPgXjoqlcpYpRFVoFQq\nERUVBSEEoqKiMGbMGADA3Llz8eSTT0pcHRGRnve6atiwIRo2bGiwi//0009aP69ZswZNmjTBsWPH\n0KdPn0pfc+jQIfj6+mL69OkA7geCiRMn4uOPPzZYXVLSd9gKAFq0aAG5XI7i4mJkZmby5qpkEuqQ\n86CioiI0bdq0wnEiIqnovY+OMeXl5QEAPDw8qmwTEBCAtLQ0xMXFQQiBzMxMbN26FS+88EKl7YuL\ni5Gfn6/1MGf6Li0HAFtbWzRv3hwAh6/INCoLOWo3b960mH94EFHdZzZBR6VSYebMmejduzc6d+5c\nZbvevXtjw4YNCA0NhZ2dHZo2bQp3d3csW7as0vbz5s2Dm5ub5qHrvBep6Lu0XI0rr8hUHhVy1KKi\nogwyj4+IqLbMJuhMmTIFZ86cwaZNmx7ZLjU1FTNmzEBUVBSOHTuGn376CVevXsWkSZMqbT937lzk\n5eVpHmlpacYo32BqMnQFcOUVmYYuIUeNYYeIzIFMCCGkLmLq1KnYuXMnfv75Z/j5+T2y7ZgxY1BU\nVIRt27ZpjiUnJ+PZZ59Fenp6tfNT8vPz4ebmhry8PLi6uhqkfkMRQqB+/fooLCzEhQsX0LZtW51f\nq/5SmThxomajNiJDk8vl0OevDJlMxgnyRGQQNf3+lrRHRwiBqVOnYseOHdi3b1+1IQcA7t69Cxsb\n7TnU6tVJZpDZaiUzMxOFhYWQy+WaHhpdqZeYc+iKjCkmJsao7YmIDE3SoDNlyhSsX78eGzduRP36\n9XHz5k3cvHlT675Zc+fORVhYmObnIUOGYPv27Vi+fDn+/PNPpKSkYPr06ejVqxeaNWsmxdswGPX8\nnJYtW8LOzk6v13LoikwhMjISEREROrVVKBSIjIw0ckVERI+m1/JyQ1u+fDkA4LnnntM6Hhsbi7Fj\nxwIAMjIycP36dc1zY8eORUFBAZYuXYpZs2bB3d0d/fr1s4hVHjWdnwNoBx0hBGQymSFLIwIA7Nq1\nCxs3bqy2HUMOEZkLSYOOLkNNa9asqXBs2rRpmDZtmhEqklZNlpareXt7QyaT4d69e8jKyoKnp6eh\nyyMrt379eowdOxbl5eUYNmwYunbtCoVCUaEdQw4RmRNJgw5pq+nScuD+zVWbNWuGGzdu4Nq1aww6\nZFDLli3D1KlTAQBhYWFYvXo1bGxsYGNjo7UKiyGHiMyN2Swvp9oNXQGcp0OGJ4TAhx9+qAk506ZN\nQ2xsrGZBQGRkJBQKBWQyGUMOEZklBh0zUpseHYA39yTDEkJg9uzZ+L//+z8A97cwWLJkCeRy7b82\nIiMjoVKpGHKIyCxx6MpM5OTk4Pbt2wCAVq1a1egc3B2ZDKW8vBwTJ07E6tWrAQD//e9/MXPmTImr\nIiLSH4OOmVD35jRr1gxOTk41OgeHrsgQSkpKMHr0aGzduhVyuRyrVq3SeUk5EZG5YdAxE7WdnwNw\n6Ipqr7CwECNGjEB8fDxsbW2xadMmDB8+XOqyiIhqjEHHTNR2fg6gPXTFvXRIX7m5uRg8eDBSUlLg\n5OSEHTt2YMCAAVKXRURUK5yMbCZqs4eOWsuWLQHc/1d5dna2Qeoi65CZmYm+ffsiJSUF7u7uSExM\nZMghIovAoGMmDDF05eDggKZNmwLg8BXp7vr163j22Wdx4sQJeHp64uDBg3j66aelLouIyCAYdMyE\nIYauAK68Iv2cP38evXv3xsWLF+Hj44NffvkFXbt2lbosIiKDYdAxAwUFBcjMzARQu6ErgCuvSHfH\njx/Hs88+i7/++gvt27dHcnIy2rRpI3VZREQGxaBjBtTDVo0aNYKbm1utzsWgQ5VRKpWQy+VQKpUA\ngF9++QV9+/bFrVu38Pjjj+Pnn39GixYtJK6SiMjwuOrKDBhifo6aeok5h65ITalUau5HFRUVhT/+\n+APbt29HUVER+vTpgx9++KHWAZuIyFwx6JgBQ83PAdijQ9oeDDlq69evBwAMGjQIW7duhaOjoxSl\nERGZBIeuzIAhlparPRh0hBC1Ph/VXZWFnAc98cQTDDlEZPEYdMyAIXt01HvpFBQUIDc3t9bno7qp\nupADADExMZo5O0RElopBxwwYco6Ok5MTmjRpAoDDV9ZKl5CjFhUVxbBDRBaNQUdiRUVFSEtLA2CY\noSuA83SsXXR0tFHbExHVJQw6Erty5QoAwNXVFY0aNTLIOXlzT+sWExNj1PZERHUJg47EHhy2MtRN\nOLk7snWLjIyEQqHQqa1CoUBkZKSRKyIikg6DjsQMORFZjUNX9MYbb1S7ooohh4isAYOOxAy5tFyN\nQ1fWTQiBSZMmoaioSHOT14cx5BCRtWDQkZgxe3Q4dGWdNmzYgJ07d8LW1hbx8fEVhrEYcojImnBn\nZIkZcmm5mrpHJzc3F7m5uXB3dzfYucm8paenY9q0aQDur6bq2rWr5m7k0dHRiImJYcghIqsiE1a2\nfW5+fj7c3NyQl5cHV1dXSWspLS2Fo6MjysvL8ddff6F58+YGO3ejRo2QnZ2NEydOoFu3bgY7L5kv\nIQSGDBmC3bt3o0ePHvj1119hY8N/yxCRZajp9zeHriR07do1lJeXw9HREV5eXgY9N4evrM+aNWuw\ne/du2NnZYe3atQw5RERg0JGUetjK398fcrlh/yi48sq6pKWlYebMmQDuz8Hp1KmTxBUREZkHBh0J\nGWMishpXXlkPIQQmTJiA/Px8PPXUU3j77belLomIyGww6EjIGEvL1Th0ZT1WrVqFhIQEODg4YM2a\nNahXr57UJRERmQ0GHQkZs0eHQ1fW4dq1a/j3v/8NAPjwww/Rrl07iSsiIjIvDDoSMsbScjUGHcun\nUqkwbtw43LlzB71798aMGTOkLomIyOww6EikvLxcazKyoann6OTk5KCgoMDg5yfprVy5Evv27YOj\noyNiY2M5ZEVEVAkGHYncuHEDJSUlsLW1hbe3t8HP7+rqigYNGgDgPB1L9Oeff2L27NkAgPnz56NN\nmzYSV0REZJ4YdCSi7s3x8/Mz2n4nHL6yTCqVChERESgsLESfPn0wdepUqUsiIjJbDDoSMeZEZDUu\nMbdMS5cuxc8//wxnZ2fExsYafA8mIiJLwr8hJWLMpeVqXGJueS5evIg5c+YAABYuXIhWrVpJXBER\nkXlj0JGIKXp0OHRlWcrLyxEREYGioiIEBQVh4sSJUpdERGT2GHQkYsyl5WocurIsS5YsQUpKClxc\nXCSuAkQAACAASURBVLB69WoOWRER6YB/U0pACGHSHh0OXdV958+fx3vvvQcA+PTTTzUhloiIHo1B\nRwKZmZkoLCyEXC7XhBFjUJ/777//RmFhodGuQ8ZVXl6OsWPH4t69exgwYAAmTJggdUlERHUGg44E\n1L05LVu2hJ2dndGu4+7uDldXVwDs1anLFi1ahMOHD8PV1RWrVq2CTCaTuiQiojqDQUcCppifo8bh\nq7rt7NmziIqKAgAsXrzYKJtLEhFZMgYdCZhiabkaV17VXaWlpQgPD0dJSQkGDRqEsWPHSl0SEVGd\nw6AjAVNMRFbjyivDUCqVkMvlUCqVJrvmggULcOzYMbi7u+PLL7/kkBURUQ0Y594D9EgcuqpblEql\nZvhI/b+RkZFGveapU6cQExMDAPj888/RrFkzo16PiMhSsUdHAqbs0eHQVe08GHLUoqKijNqzox6y\nKi0txdChQ/H6668b7VpERJaOQcfEcnJycPv2bQAwyfb9DDo1V1nIUTN02HlwaOyjjz7CiRMn4OHh\ngRUrVnDIioioFjh0ZWLq3pxmzZrBycnJ6NdTz9HJzMxEUVERHB0djX5NS/CokKNmqGGsh4fG1Dse\nL1u2DE2bNq3VuYmIrB17dEzMlPNzAMDDwwMuLi4AgOvXr5vkmnWdLiFHLSoqCmPGjEFqamqNNmWs\n7FoqlQodO3ZEaGio3ucjIiJt7NExMVMuLQcAmUwGX19fnDlzBlevXkW7du1Mct26LDo6Wq/269ev\nx/r16wEADRs2hI+PT5UPDw8PzVDUowJVamoqPvjgA6NPeiYisnQMOiZmyonIaj4+PpqgQ9WLiYnR\nuUcHADw9PXHv3j3k5eUhOzsb2dnZOH78eKVtnZ2d4ePjg5KSEs3vQlVMtcKLiMiSMeiYmKmHrgAu\nMdeXOljoEnYUCoWmfV5eHq5du1blQ32Ps9TUVJ1rYdghIqodBh0Tk6JHhyuv9KfL3cEfDDkA4Obm\nhq5du6Jr166Vtr937x6uX7+O9u3bQwihcy3R0dEMOkRENcTJyCZUUFCAzMxMAKabowNwd2R9bd68\nGREREQCAXr16Vdrm4ZCjCwcHB7Rt21azEaCu9G1PRET/YNAxIfWwVaNGjeDm5may63LoSnc7duzA\n66+/DpVKhQkTJuDQoUNQKBRabWoSch4UGRlZ4ZxVqe21iIisHYOOCUkxPwf4J+ikp6ejuLjYpNeu\nS3bv3o3Q0FCUl5djzJgxWLlyJeRyuSaYyGQygwUPXcIOQw4RUe0x6JiQqZeWqzVq1EizUSD30qlc\nYmIiRowYgdLSUoSGhuLrr7/WbNwH3A8mKpXKoMHjUWGHIYeIyDAkDTrz5s1Dz549Ub9+fTRp0gTD\nhg3DhQsXqn1dcXEx3nvvPfj4+MDe3h6+vr74+uuvTVBx7UgxERn4Zy8dgMNXlTl48CCGDh2K4uJi\nDBs2DOvWrYONjWnm6VcWdhhyiIgMR9JVVwcPHsSUKVPQs2dPlJWV4d1338WAAQOQmpoKZ2fnKl83\ncuRIZGZmYvXq1WjdujUyMjKgUqlMWHnNSBV0gPvDV+fOneOE5If873//w6BBg1BUVIQXXngBmzZt\ngq2trUlrUIea6OhoxMTEMOQQERmQpEHnp59+0vp5zZo1aNKkCY4dO4Y+ffpU+ZqDBw/izz//hIeH\nB4B/5qCYO6nm6ABceVWZo0ePYuDAgSgsLERwcDC2b98Oe3t7SWqJjIxkwCEiMgKzmqOTl5cHAJoA\nU5kffvgBTzzxBBYsWPD/2rv3qKjK/X/g72EQhhBJRWSGm3hBEsW8p/bVEkI8HcWsvGGi6FnLDpTY\nycxzDqDQiaxjNzPMVEzNS7a8RUsRUTBP3lI5Sbq8H1AEDOXuBZx5fn/0GwIlmHH2Zi68X2uxknHz\n2R/Jx3nzPM/eG56envD398ebb76JO3futFSbj+TOnTu4evUqgJbfowPwyqsH5eTkYPTo0aioqMCI\nESOwc+dOqFQqc7dFREQSs5gbBup0OsTGxmL48OHo3bv3Hx53+fJlHDp0CCqVCtu3b0dJSQn++te/\n4ubNm0hNTX3o+Hv37jW40qiiokKW/ptz5coVAEC7du3g5ubW4ufnTQN/98svv+C5555DaWkphg4d\nirS0tBZ5kjwREbU8i5nRiY6ORm5uLjZv3tzkcTqdDgqFAl9//TUGDx6MP/3pT/jwww/x1VdfNTqr\nk5ycDFdX17oPb29vuf4ITaq/bKV/qGNLYtD5zfnz5xEcHIySkhIMHDgQu3fvhouLi7nbIiIimVhE\n0ImJiUFaWhoOHDgALy+vJo9Vq9Xw9PRscMO9J554AkIIXLt27aHjFy5ciPLy8roP/fJRSzPnRmTg\n9z06169fR01NjVl6MLdLly5h1KhRKC4uRt++fZGent6iN24kIqKWZ9agI4RATEwMtm/fjv3798PP\nz6/Zrxk+fDiuX7+OqqqqutfOnz8POzu7RkOSo6Mj2rVr1+DDHMx1Dx29zp07Q6VSQafTNRoIbV1e\nXh5GjRqFgoIC9OrVCxkZGU3uBSMiIttg1qATHR2NDRs2YOPGjXBxcUFRURGKiooaLEEtXLgQ06dP\nr/t86tSp6NixI2bOnIkzZ87g4MGDmD9/PqKioupuimeJzD2jo1AozH7lVVJSEuzs7JCUlNSi5y0o\nKEBwcDDy8/Ph7++PzMxMdOrUqUV7ICIi8zBr0ElJSUF5eTmeeeYZqNXquo8tW7bUHVNYWNjgbr5t\n27ZFRkYGysrKMHDgQERERGDs2LH49NNPzfFHMJg5Ly3X0wcdc1x5lZSUhPj4eAghEB8f32Jhp7i4\nGMHBwbh06RL8/PyQmZkJDw+PFjk3ERGZn1mvuhJCNHvM2rVrH3otICAAGRkZMnQkj9ra2rpZFHMt\nXQHm25CsDzn16T+X8t4xSUlJDW66V1JSgpCQEJw7dw4+Pj7Yv39/s3vAiIjItljM5eW2LC8vD1qt\nFk5OTlCr1WbrwxxBp7GQoydl2Kl/nvj4eNy5cwe7d+9Gbm4uNBoNMjMzrebGkkREJB0GnRagX7bq\n1q1bgwdFtrSW3qPTVMjRkyLsNHae5ORkAIC7uzsyMzPNumRIRETmYxGXl9s6c29E1mvJuyMbEnL0\n4uPj6zaXl5aWGrSkaeh5Xn75ZQQEBBhcj4iIbAtndFqAuS8t19MHnWvXruH+/fuyPqE7ISHBqOPX\nrl1btx/L0dERHh4eUKvVD/23/q9XrVqFRYsWNVl3+fLl6Ny5M58jRUTUSjHotABLmdHx8PCAg4MD\nampqcO3aNVn3rCxevNjgGR0AcHNzg1arRWlpKe7du4e8vDzJZp7k2PhMRETWgUGnBVjCpeUAYGdn\nBx8fH1y8eBF5eXmyBh19qDAk7CQmJtYdf/fuXRQVFaGwsLDuv439+vr160b1k5CQwKBDRNQKMejI\nTKvVNtiMbG5dunTBxYsX8b///Q8jR46U9VyGhJ36IQcAVCoVunTp0mwIW7x4cbPLVg8eT0RErQ83\nI8usoKAANTU1aNOmjdkeKFpfS195FRcXB39//0Z/78GQY4yEhAQkJiYadKwp5yEiIuvGoCMz/WyO\nn5+frJt/DdWSV14Bv2181u9Rqk+K8BEXF9ds2GHIISJq3Rh0ZGYpG5H1WvqmgWvXroVOp8OIESOQ\nmJgIhUIhafhoKuww5BARkfmnGGycpVxarteSQUen02HNmjUAgFmzZmH69OmyBI/G9gIx5BAREcAZ\nHdlZ2oyOfo/O1atXodVqZT3XgQMHcOXKFbRr1w4vvfSSrOfSz+xIPWNERETWjUFHZpZyabmeRqOB\nvb097t+/b/Ql2sZatWoVACAiIgKPPfaYrOcCfgs7Op2OIYeIiOow6MhICGFxS1dKpRI+Pj4A5F2+\nunnzJrZt2wYAmD17tmznISIiagqDjoyKi4tRXV0NOzs7i3pytn75Ss4rrzZs2ICamhr069cP/fv3\nl+08RERETWHQkZF+NsfHxweOjo5m7uZ3cm9IFkLULVvNmjVLlnMQEREZgkFHRpa2P0dP7qBz/Phx\n5ObmQqVSYerUqbKcg4iIyBAMOjKytP05enLfHVk/m/PSSy+hffv2spyDiIjIEAw6MrK0S8v15Lw7\nclVVFTZt2gSAm5CJiMj8GHRkZOlLV3l5edDpdJLW3rp1K6qqqtC9e3eMGDFC0tpERETGYtCRkaXO\n6Hh6ekKpVKK2thaFhYWS1q6/CVmhUEham4iIyFgMOjK5desWSktLAQBdu3Y1czcN2dvbw8vLC4C0\ny1dnzpzBjz/+CKVSicjISMnqEhERPSoGHZnoZ3M0Gk2L3BXYWHJcebV69WoAwJ///Geo1WrJ6hIR\nET0qBh2ZWOr+HD2pr7yqqanBunXrAHATMhERWQ4GHZlY6qXlelJfebVr1y6UlJRArVYjLCxMkppE\nRESmYtCRiaVuRNaTeulKvwl55syZsLe3l6QmERGRqRh0ZNKalq7y8vKwd+9eAEBUVJTJ9YiIiKTC\noCMTa5nRyc/PhxDCpFpr166FEAKjRo2y2KU6IiJqnRh0ZFBZWYni4mIAlrtHx8vLC3Z2drh7925d\nr49Cq9VizZo1APgATyIisjwMOjLQL1u5ubnB1dXVzN00zsHBAZ6engBMW77at28f8vPz0b59e0yY\nMEGi7oiIiKTBoCMDS9+fo6ffp2PKlVf6TcjTpk2DSqWSpC8iIiKpMOjIwNIvLdcz9cqrX3/9FTt3\n7gTAe+cQEZFlYtCRgaVvRNYzNeisX78etbW1GDhwIIKCgqRrjIiISCIMOjKwtqWrRwk6Qoi6ZSvO\n5hARkaVi0JGBtc3oPMoencOHD+Ps2bN47LHHMGXKFIk7IyIikgaDjsTu3LmDq1evArCuPTrG3ktH\n/wDPiRMnol27dlK3RkREJAkGHYm99dZbAABHR0e4ubmZuZumeXt7A/gtnP36668Gf11FRQU2b94M\ngMtWRERk2Rh0JJSUlITPPvsMAHDv3j288847Zu6oaY6OjtBoNACMW77asmULbt++jZ49e2LYsGFy\ntUdERGQyBh2JJCUlIT4+vsFr8fHxSEpKMlNHhnmUK6/qb0JWKBQydEVERCQNBh0JNBZy9Cw97Bh7\n5dXp06dx7Ngx2NvbY/r06TJ2RkREZDoGHRM1FXL0LDnsGHvllX4Tcnh4ONzd3eVqi4iISBIMOiYw\nJOToWWrYMWbp6u7du1i/fj0APsCTiIisA4OOCRISEmQ9viUYs3S1Y8cO3Lp1C15eXggNDZW5MyIi\nItMx6Jhg8eLFsh7fEuovXTV3Lx39JuSoqCgolUq5WyMiIjIZg44J4uLikJiYaNCxiYmJiIuLk7kj\n4/n4+AAAqqqqcOvWrT887sqVK8jMzIRCocDMmTNbqj0iIiKTMOiYyJCwY6khBwCcnJzg4eEBoOnl\nqzVr1gAAnnvuubpZICIiIkvHoCOBpsKOJYccPf0+nT+68ur+/ftITU0FwE3IRERkXRh0JNJY2LGG\nkAM0f+VVeno6CgoK0LFjR4SHh7dcY0RERCZi0JGQPuwoFAqrCTlA80FHf++c6dOnw9HRsYW6IiIi\nMp29uRuwNXFxcVYTcPSaWroqKirCd999B4DLVkREZH04o0NNzuisW7cO9+/fx1NPPYXAwMCWbYyI\niMhEDDrUIOjUv5eOEKJu2Wr27NnmaI2IiMgkDDpUdy+diooKlJWV1b1+6NAhnD9/Hm3btsWkSZPM\n1R4REdEjY9AhODs7o1OnTgAa7tPR3wl58uTJaNu2rVl6IyIiMgWDDgF4eJ9OWVkZtm7dCoDLVkRE\nZL0YdAjAww/33LRpE+7cuYPAwEAMHjzYjJ0RERE9OgYdAtDw4Z4AGmxCVigU5mqLiIjIJGYNOsnJ\nyRg0aBBcXFzg7u6O8ePH49y5cwZ//X/+8x/Y29vjySeflLHL1qH+0tWpU6dw4sQJODg4YNq0aeZt\njIiIyARmDTrZ2dmIjo7GkSNHkJGRgdraWoSGhqK6urrZry0rK8P06dMRHBzcAp3aPv3S1Y4dOzBn\nzhwAwAsvvAA3NzdztkVERGQSs94Zec+ePQ0+X7t2Ldzd3XHixAmMGDGiya+dM2cOpk6dCqVSiR07\ndsjZZqtQ///FsWPHAPBOyEREZP0sao9OeXk5AKBDhw5NHpeamorLly8jISGhJdqyeUlJSVi+fPlD\nrx8+fNgM3RAREUnHYp51pdPpEBsbi+HDh6N3795/eNyFCxfw9ttv44cffoC9ffPt37t3D/fu3av7\nvKKiQpJ+bUVSUhLi4+Mb/b2EhAQoFAqre3YXERGRnsXM6ERHRyM3NxebN2/+w2O0Wi2mTp2KxYsX\nw9/f36C6ycnJcHV1rfvw9vaWqmWr11TI0YuPj0dSUlILdURERCQthaj/cCMziYmJwc6dO3Hw4EH4\n+fn94XFlZWVo3749lEpl3Ws6nQ5CCCiVSuzduxejRo1q8DWNzeh4e3ujvLwc7dq1k/4PYyUMCTn1\nJSYmcmaHiIjMpqKiAq6urka/f5s16Agh8Nprr2H79u3IyspCjx49mjxep9PhzJkzDV77/PPPsX//\nfnz77bfw8/ODs7NzkzUe9Rtla+zs7GDM/3qFQgGdTidjR0RERH/sUd+/zbpHJzo6Ghs3bsTOnTvh\n4uKCoqIiAICrqyucnJwAAAsXLkRBQQHWrVsHOzu7h/bvuLu7Q6VSNbmvhx62ePFio2Z0Fi9eLGM3\nRERE8jDrHp2UlBSUl5fjmWeegVqtrvvYsmVL3TGFhYXIz883Y5e2KS4uDomJiQYdy2UrIiKyVhax\nR6clcemqoeb26jDkEBGRJXjU92+LueqKzKOpmR2GHCIisnYMOtRo2GHIISIiW8CgQwB+DzsKhYIh\nh4iIbAb36BAREZHF4x4dIiIiogcw6BAREZHNYtAhIiIim8WgQ0RERDaLQYeIiIhsFoMOERER2SwG\nHSIiIrJZDDpERERks+zN3UBL098fsaKiwsydEBERkaH079vG3ue41QWdmzdvAgC8vb3N3AkREREZ\nq7KyEq6urgYf3+qCTocOHQAA+fn5Rn2jDFVRUQFvb29cvXpVlkdMyFnfmnuXu7419y53fWvu3drr\nW3Pvcte35t7lrm+tvQshUFlZCY1GY9TXtbqgY2f327YkV1dXWZ911a5dO6utb829y13fmnuXu741\n927t9a25d7nrW3Pvcte3xt4fZYKCm5GJiIjIZjHoEBERkc1SLlq0aJG5m2hpSqUSzzzzDOzt5Vm5\ns+b61ty73PWtuXe561tz79Ze35p7l7u+Nfcud31r7t1YCmHsdVpEREREVoJLV0RERGSzGHSIiIjI\nZjHoEBERkc1i0CEiIiKb1eqCzvLly9GlSxeoVCoMGTIEx44dk6TuwYMHMXbsWGg0GigUCuzYsUOS\nugCQnJyMQYMGwcXFBe7u7hg/fjzOnTsnWf2UlBQEBQXV3dxp6NCh2L17t2T163vvvfegUCgQGxsr\nSb1FixZBoVA0+AgICJCktl5BQQGmTZuGjh07wsnJCX369MFPP/0kSe0uXbo81L9CoUB0dLTJtbVa\nLeLi4uDn5wcnJyd069YNSUlJRj8npimVlZWIjY2Fr68vnJycMGzYMBw/fvyRajU3hoQQiI+Ph1qt\nhpOTE0JCQnDhwgXJ6m/btg2hoaHo2LEjFAoFcnJyJKldW1uLBQsWoE+fPnB2doZGo8H06dNx/fp1\nyXpftGgRAgIC4OzsjPbt2yMkJARHjx6VrH59c+bMgUKhwMcffyxJ7RkzZjz09z8sLEzS3s+ePYtx\n48bB1dUVzs7OGDRoEPLz8yWp39j4VSgU+OCDD0yuXVVVhZiYGHh5ecHJyQm9evXCihUrDOrbkPrF\nxcWYMWMGNBoNHnvsMYSFhRk8pgx5XzJ1zEqlVQWdLVu24I033kBCQgJOnjyJvn37YvTo0bhx44bJ\ntaurq9G3b18sX75cgk4bys7ORnR0NI4cOYKMjAzU1tYiNDQU1dXVktT38vLCe++9hxMnTuCnn37C\nqFGjEB4ejl9++UWS+nrHjx/HF198gaCgIEnrBgYGorCwsO7j0KFDktUuLS3F8OHD0aZNG+zevRtn\nzpzB0qVL0b59e0nqHz9+vEHvGRkZAICXX37Z5NpLlixBSkoKPvvsM5w9exZLlizB+++/j2XLlplc\nW2/27NnIyMjA+vXrcfr0aYSGhiIkJAQFBQVG12puDL3//vv49NNPsWLFChw9ehTOzs4YPXo07t69\nK0n96upqPP3001iyZImkvd++fRsnT55EXFwcTp48iW3btuHcuXMYN26cJPUBwN/fH5999hlOnz6N\nQ4cOoUuXLggNDcWvv/4qSX297du348iRI0bdgt+Q2mFhYQ3GwaZNmySrf+nSJTz99NMICAhAVlYW\nfv75Z8TFxUGlUklSv37fhYWFWLNmDRQKBV588UWTa7/xxhvYs2cPNmzYgLNnz2LevHmIiYnBrl27\nTO5dCIHx48fj8uXL2LlzJ06dOgVfX1+EhIQY9N5iyPuSqWNWMqIVGTx4sIiOjq77XKvVCo1GI5KT\nkyU9DwCxfft2SWvWd+PGDQFAZGdny3aO9u3bi1WrVklWr7KyUvTo0UNkZGSIkSNHirlz50pSNyEh\nQfTt21eSWo1ZsGCBePrpp2Wr/6C5c+eKbt26CZ1OZ3Kt559/XkRFRTV4bcKECSIiIsLk2kIIcfv2\nbaFUKkVaWlqD1/v37y/+8Y9/mFT7wTGk0+mEh4eH+OCDD+peKysrE46OjmLTpk0m16/vypUrAoA4\ndeqU8Y03U1vv2LFjAoDIy8uTpX55ebkAIPbt2ydZ/WvXrglPT0+Rm5srfH19xUcffSRJ7cjISBEe\nHm50LUPrT5o0SUybNk22+g8KDw8Xo0aNkqR2YGCgSExMbPDao46vB+ufO3dOABC5ubl1r2m1WtGp\nUyfx5ZdfGl3/wfclqcesKVrNjE5NTQ1OnDiBkJCQutfs7OwQEhKCw4cPm7Ez45WXlwP4/QGlUtJq\ntdi8eTOqq6sxdOhQyepGR0fj+eefb/D9l8qFCxeg0WjQtWtXREREGDwlbYhdu3Zh4MCBePnll+Hu\n7o5+/frhyy+/lKx+fTU1NdiwYQOioqKgUChMrjds2DBkZmbi/PnzAID//ve/OHToEMaMGWNybQC4\nf/8+tFrtQz8ZOzk5STqrBgBXrlxBUVFRg78/rq6uGDJkiNWNX+C3MaxQKPD4449LXrumpgYrV66E\nq6sr+vbtK0lNnU6HV155BfPnz0dgYKAkNevLysqCu7s7evbsiVdffRU3b96UpK5Op8P3338Pf39/\njB49Gu7u7hgyZIikWwvqKy4uxvfff49Zs2ZJUm/YsGHYtWsXCgoKIITAgQMHcP78eYSGhppc+969\newDQYPza2dnB0dHxkcbvg+9LljRmW03QKSkpgVarRefOnRu83rlzZxQVFZmpK+PpdDrExsZi+PDh\n6N27t2R1T58+jbZt28LR0RFz5szB9u3b0atXL0lqb968GSdPnkRycrIk9eobMmQI1q5diz179iAl\nJQVXrlzB//3f/6GyslKS+pcvX0ZKSgp69OiB9PR0vPrqq3j99dfx1VdfSVK/vh07dqCsrAwzZsyQ\npN7bb7+NyZMnIyAgAG3atEG/fv0QGxuLiIgISeq7uLhg6NChSEpKwvXr16HVarFhwwYcPnwYhYWF\nkpxDTz9GrX38AsDdu3exYMECTJkyRdIHHqalpaFt27ZQqVT46KOPkJGRATc3N0lqL1myBPb29nj9\n9dclqVdfWFgY1q1bh8zMTCxZsgTZ2dkYM2YMtFqtybVv3LiBqqoqvPfeewgLC8PevXvxwgsvYMKE\nCcjOzpag+4a++uoruLi4YMKECZLUW7ZsGXr16gUvLy84ODggLCwMy5cvx4gRI0yuHRAQAB8fHyxc\nuBClpaWoqanBkiVLcO3aNaPHb2PvS5Y0Zs1/b2YySnR0NHJzcyX/iblnz57IyclBeXk5vv32W0RG\nRiI7O9vksHP16lXMnTsXGRkZBq+JG6P+7ERQUBCGDBkCX19ffPPNN5L8VKXT6TBw4EC8++67AIB+\n/fohNzcXK1asQGRkpMn161u9ejXGjBlj1P6HpnzzzTf4+uuvsXHjRgQGBiInJwexsbHQaDSS9b5+\n/XpERUXB09MTSqUS/fv3x5QpU3DixAlJ6tua2tpaTJw4EUIIpKSkSFr72WefRU5ODkpKSvDll19i\n4sSJOHr0KNzd3U2qe+LECXzyySc4efKkJDOND5o8eXLdr/v06YOgoCB069YNWVlZCA4ONqm2TqcD\nAISHh2PevHkAgCeffBI//vgjVqxYgZEjR5pU/0Fr1qxBRESEZP/WLVu2DEeOHMGuXbvg6+uLgwcP\nIjo6GhqNxuTZ8TZt2mDbtm2YNWsWOnToAKVSiZCQEIwZM8boCxbkel+SSquZ0XFzc4NSqURxcXGD\n14uLi+Hh4WGmrowTExODtLQ0HDhwAF5eXpLWdnBwQPfu3TFgwAAkJyejb9+++OSTT0yue+LECdy4\ncQP9+/eHvb097O3tkZ2djU8//RT29vaS/NRW3+OPPw5/f39cvHhRknpqtfqhsPfEE09IujwGAHl5\nedi3bx9mz54tWc358+djwYIFmDx5Mvr06YNXXnkF8+bNk3RmrVu3bsjOzkZVVRWuXr2KY8eOoba2\nFl27dpXsHADqxqg1j199yMnLy0NGRoakszkA4OzsjO7du+Opp57C6tWrYW9vj9WrV5tc94cffsCN\nGzfg4+NTN4bz8vLwt7/9DV26dDG98Qd07doVbm5ukoxhNzc32Nvbt8gY/uGHH3Du3DnJxvCdO3fw\n97//HUuXLsXYsWMRFBSEmJgYTJo0Cf/+978lOceAAQOQk5ODsrIyFBYWYs+ePbh586ZR4/eP3pcs\nacy2mqDj4OCAAQMGIDMzs+41nU6HzMxMSfeiyEEIgZiYGGzfvh379++Hn5+f7OfU6XR1a7im3nvC\nUAAABhFJREFUCA4OxunTp5GTk1P3MXDgQERERCAnJwdKpVKCbn9XVVWFixcvQq1WS1Jv+PDhD10y\nef78efj6+kpSXy81NRXu7u54/vnnJat5+/bthx6op1Qq637KlZKzszPUajVKS0uRnp6O8PBwSev7\n+fnBw8OjwfitqKjA0aNHLX78Ar+HnAsXLmDfvn3o2LGj7OeUagy/8sor+PnnnxuMYY1Gg/nz5yM9\nPV2CThu6du0abt68KckYdnBwwKBBg1pkDK9evRoDBgyQbF9UbW0tamtrW2QMu7q6olOnTrhw4QJ+\n+ukng8Zvc+9LljRmW9XS1RtvvIHIyEgMHDgQgwcPxscff4zq6mrMnDnT5Nr6N1i9K1euICcnBx06\ndICPj49JtaOjo7Fx40bs3LkTLi4udeubrq6ucHJyMqk2ACxcuBBjxoyBj48PKisrsXHjRmRlZUny\nj5iLi8tDe4mcnZ3RsWNHSfYYvfnmmxg7dix8fX1x/fp1JCQkwN7eHlOmTDG5NgDMmzcPw4YNw7vv\nvouJEyfi2LFjWLlyJVauXClJfeC3N6TU1FRERkZK+qTfsWPH4p133oG3tzcCAwNx6tQpfPjhh4iK\nipLsHOnp6RBCoGfPnrh48SLmz5+PgICARxpTzY2h2NhYvPPOO+jRowf8/PwQFxcHjUaD8ePHS1L/\n1q1byM/Pr7u/jf7N0cPDo9mfQJuqrVar8dJLL+HkyZNIS0uDVqutG8MdOnSAg4ODSb137NgR//rX\nvzBu3Dio1WqUlJRg+fLlKCgoMPg2Bc19bx4MZm3atIGHhwd69uxpUu0OHTpg8eLFePHFF+Hh4YFL\nly7hrbfeQvfu3TF69GhJep8/fz4mTZqEESNG4Nlnn8WePXvw3XffISsrS5L6wG9v4Fu3bsXSpUsN\nqmlo7ZEjR+LNN9+ESqWCr68vsrOzsW7dOnz44YeS1N+6dSs6deoEHx8fnD59GnPnzsX48eMN2uzc\n3PuS/n5ppoxZybToNV4WYNmyZcLHx0c4ODiIwYMHiyNHjkhS98CBAwLAQx+RkZEm126sLgCRmppq\ncm0hhIiKihK+vr7CwcFBdOrUSQQHB4u9e/dKUrsxUl5ePmnSJKFWq4WDg4Pw9PQUkyZNEhcvXpSk\ntt53330nevfuLRwdHUVAQIBYuXKlpPXT09MFAHHu3DlJ61ZUVIi5c+cKHx8foVKpRNeuXcU//vEP\nce/ePcnOsWXLFtG1a1fh4OAgPDw8RHR0tCgrK3ukWs2NIZ1OJ+Li4kTnzp2Fo6OjCA4ONup71lz9\n1NTURn8/ISHBpNr6y9Ub+zhw4IDJvd+5c0e88MILQqPRCAcHB6FWq8W4cePEsWPHJPvePMiYy8ub\nqn379m0RGhoqOnXqJNq0aSN8fX3FX/7yF1FUVCRp76tXrxbdu3cXKpVK9O3bV+zYsUPS+l988YVw\ncnIy+u9+c7ULCwvFjBkzhEajESqVSvTs2VMsXbrU4NtPNFf/k08+EV5eXqJNmzbCx8dH/POf/zT4\n3wdD3pdMHbNSUfz/homIiIhsTqvZo0NEREStD4MOERER2SwGHSIiIrJZDDpERERksxh0iIiIyGYx\n6BAREZHNYtAhIiIim8WgQ0RERDaLQYeIrN6MGTMeuq38t99+C5VKZfRt+YnItrSqZ10RUeuwatUq\nREdHY8WKFZI8y46IrBdndIjIprz//vt47bXXsHnzZoYcIuKMDhHZjgULFuDzzz9HWloagoODzd0O\nEVkABh0isgm7d+/Gzp07kZmZiVGjRpm7HSKyEFy6IiKbEBQUhC5duiAhIQFVVVXmboeILASDDhHZ\nBE9PT2RlZaGgoABhYWGorKw0d0tEZAEYdIjIZvj6+iI7OxtFRUUMO0QEgEGHiGyMt7c3srKycOPG\nDYwePRoVFRXmbomIzIhBh4hsjpeXF7KyslBSUsKwQ9TKKYQQwtxNEBEREcmBMzpERERksxh0iIiI\nyGYx6BAREZHNYtAhIiIim8WgQ0RERDaLQYeIiIhsFoMOERER2SwGHSIiIrJZDDpERERksxh0iIiI\nyGYx6BAREZHNYtAhIiIim/X/AAjtT1GFmU0AAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ae2c42c358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best value of K is 3 with an error of 2.3933%\n",
      "\n",
      "K = 3 will be used for the testing set:\n",
      "Testing Confusion Matrix: Actual vs. Prediction\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>974</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1132</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>997</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>978</td>\n",
       "      <td>1</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>952</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>860</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>945</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>17</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>997</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>16</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>920</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>967</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1    2    3    4    5    6    7    8    9\n",
       "0  974     1    1    0    0    1    2    1    0    0\n",
       "1    0  1132    2    0    0    0    1    0    0    0\n",
       "2    9     8  997    2    1    0    0   14    1    0\n",
       "3    1     2    3  978    1   12    0    7    3    3\n",
       "4    1     5    0    0  952    0    4    2    0   18\n",
       "5    6     1    0   11    1  860    5    1    3    4\n",
       "6    5     3    0    0    2    3  945    0    0    0\n",
       "7    0    17    5    0    1    0    0  997    0    8\n",
       "8    7     2    4   16    7    9    3    3  920    3\n",
       "9    4     4    2    9   10    2    1    9    1  967"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>digit</th>\n",
       "      <th>error per digit in %</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.6122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.2643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3.3915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3.1683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>3.0550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>3.5874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1.3570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>3.0156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>5.5441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>4.1625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   digit  error per digit in %\n",
       "0      0                0.6122\n",
       "1      1                0.2643\n",
       "2      2                3.3915\n",
       "3      3                3.1683\n",
       "4      4                3.0550\n",
       "5      5                3.5874\n",
       "6      6                1.3570\n",
       "7      7                3.0156\n",
       "8      8                5.5441\n",
       "9      9                4.1625"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The overall testing error is 2.78% for k = 3.\n"
     ]
    }
   ],
   "source": [
    "result_pca_low = knn_loocv_method(train_PCA_low, train_label, test_PCA_low, test_label, k_list=range(1, 21))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 87)"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_PCA_low_1 = np.dot(train, basis_vecs[0][:,0:87])\n",
    "train_PCA_low_1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 87)"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_PCA_low_1 = np.dot(test, basis_vecs[0][:,0:87])\n",
    "test_PCA_low_1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LOOCV and testing analysis having reduced the dimension of the dataset to 87  (90% Variance Explained): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAHHCAYAAAC2rPKaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1v8BRdn68YURckcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ae1e234ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best value of K is 3 with an error of 2.26%\n",
      "\n",
      "K = 3 will be used for the testing set:\n",
      "Testing Confusion Matrix: Actual vs. Prediction\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>974</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1131</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>1002</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>977</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>952</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>866</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>945</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>998</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "      <td>6</td>\n",
       "      <td>13</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>921</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>969</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1     2    3    4    5    6    7    8    9\n",
       "0  974     1     1    0    0    1    2    1    0    0\n",
       "1    0  1131     3    0    0    0    1    0    0    0\n",
       "2    7     4  1002    2    1    0    0   14    2    0\n",
       "3    0     1     5  977    1   11    0    7    5    3\n",
       "4    2     6     0    0  952    0    4    2    0   16\n",
       "5    3     1     0    9    2  866    4    1    2    4\n",
       "6    5     3     0    0    2    3  945    0    0    0\n",
       "7    0    16     6    0    2    0    0  998    0    6\n",
       "8    6     1     3   15    6   13    3    3  921    3\n",
       "9    5     5     2    9    9    3    1    3    3  969"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>digit</th>\n",
       "      <th>error per digit in %</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.6122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.3524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2.9070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3.2673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>3.0550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>2.9148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1.3570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>2.9183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>5.4415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>3.9643</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   digit  error per digit in %\n",
       "0      0                0.6122\n",
       "1      1                0.3524\n",
       "2      2                2.9070\n",
       "3      3                3.2673\n",
       "4      4                3.0550\n",
       "5      5                2.9148\n",
       "6      6                1.3570\n",
       "7      7                2.9183\n",
       "8      8                5.4415\n",
       "9      9                3.9643"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The overall testing error is 2.65% for k = 3.\n"
     ]
    }
   ],
   "source": [
    "result_pca_low_1 = knn_loocv_method(train_PCA_low_1, train_label, test_PCA_low_1, test_label, k_list=range(1, 21))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 59)"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_PCA_low_2 = np.dot(train, basis_vecs[0][:,0:59])\n",
    "train_PCA_low_2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 59)"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_PCA_low_2 = np.dot(test, basis_vecs[0][:,0:59])\n",
    "test_PCA_low_2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LOOCV and testing analysis having reduced the dimension of the dataset to 59  (85% Variance Explained): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAHHCAYAAAC2rPKaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nk/X/AAgzMrOzLQOhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ae204795f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best value of K is 3 with an error of 2.115%\n",
      "\n",
      "K = 3 will be used for the testing set:\n",
      "Testing Confusion Matrix: Actual vs. Prediction\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>974</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1130</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>1007</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>977</td>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>959</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>863</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>945</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>999</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>17</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>925</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>973</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1     2    3    4    5    6    7    8    9\n",
       "0  974     1     1    0    0    1    2    1    0    0\n",
       "1    0  1130     3    0    0    0    1    0    0    1\n",
       "2    5     4  1007    1    1    0    1   11    2    0\n",
       "3    0     0     3  977    1   11    0    9    8    1\n",
       "4    1     1     0    0  959    0    4    1    0   16\n",
       "5    4     1     0   10    2  863    6    1    2    3\n",
       "6    5     3     0    0    2    3  945    0    0    0\n",
       "7    0    14     7    0    2    0    0  999    0    6\n",
       "8    5     0     3   17    7    7    3    3  925    4\n",
       "9    6     3     2    7    8    3    1    3    3  973"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>digit</th>\n",
       "      <th>error per digit in %</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.6122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.4405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2.4225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3.2673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>2.3422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>3.2511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1.3570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>2.8210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>5.0308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>3.5679</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   digit  error per digit in %\n",
       "0      0                0.6122\n",
       "1      1                0.4405\n",
       "2      2                2.4225\n",
       "3      3                3.2673\n",
       "4      4                2.3422\n",
       "5      5                3.2511\n",
       "6      6                1.3570\n",
       "7      7                2.8210\n",
       "8      8                5.0308\n",
       "9      9                3.5679"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The overall testing error is 2.48% for k = 3.\n"
     ]
    }
   ],
   "source": [
    "result_pca_low_2 = knn_loocv_method(train_PCA_low_2, train_label, test_PCA_low_2, test_label, k_list=range(1, 21))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LOOCV and testing analysis having reduced the dimension of the dataset to 33  (75% Variance Explained): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 33)"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_PCA_low_3 = np.dot(train, basis_vecs[0][:,0:33])\n",
    "train_PCA_low_3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 33)"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_PCA_low_3 = np.dot(test, basis_vecs[0][:,0:33])\n",
    "test_PCA_low_3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAHHCAYAAAC2rPKaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6BAREZHZYtAhIiIis/X/ANGzn5Ps+6S6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ae32d90358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best value of K is 3 with an error of 2.1433%\n",
      "\n",
      "K = 3 will be used for the testing set:\n",
      "Testing Confusion Matrix: Actual vs. Prediction\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>974</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1131</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>1009</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>974</td>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>951</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>2</td>\n",
       "      <td>864</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>945</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>14</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>992</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>14</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>936</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>967</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0     1     2    3    4    5    6    7    8    9\n",
       "0  974     1     1    0    0    1    2    1    0    0\n",
       "1    0  1131     3    0    0    0    0    0    0    1\n",
       "2    5     2  1009    1    1    0    3    9    2    0\n",
       "3    0     0     5  974    0   14    0    6    7    4\n",
       "4    1     0     0    0  951    1    2    2    1   24\n",
       "5    3     1     0   11    2  864    5    1    2    3\n",
       "6    3     4     0    0    3    2  945    0    1    0\n",
       "7    0    14    11    0    3    0    0  992    0    8\n",
       "8    3     0     4   14    3    5    3    3  936    3\n",
       "9    6     4     1    7   11    3    1    4    5  967"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>digit</th>\n",
       "      <th>error per digit in %</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0.6122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.3524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2.2287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3.5644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>3.1568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>3.1390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1.3570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>3.5019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>3.9014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>4.1625</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   digit  error per digit in %\n",
       "0      0                0.6122\n",
       "1      1                0.3524\n",
       "2      2                2.2287\n",
       "3      3                3.5644\n",
       "4      4                3.1568\n",
       "5      5                3.1390\n",
       "6      6                1.3570\n",
       "7      7                3.5019\n",
       "8      8                3.9014\n",
       "9      9                4.1625"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The overall testing error is 2.57% for k = 3.\n"
     ]
    }
   ],
   "source": [
    "result_pca_low_3 = knn_loocv_method(train_PCA_low_3, train_label, test_PCA_low_3, test_label, k_list=range(1, 21))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>% variance Explain</th>\n",
       "      <th>no of components</th>\n",
       "      <th>best K used</th>\n",
       "      <th>test error in %</th>\n",
       "      <th>query time (ms)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>99</td>\n",
       "      <td>331</td>\n",
       "      <td>1</td>\n",
       "      <td>3.12</td>\n",
       "      <td>123.0881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>155</td>\n",
       "      <td>3</td>\n",
       "      <td>2.78</td>\n",
       "      <td>50.6090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>90</td>\n",
       "      <td>87</td>\n",
       "      <td>3</td>\n",
       "      <td>2.65</td>\n",
       "      <td>36.7794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>85</td>\n",
       "      <td>59</td>\n",
       "      <td>3</td>\n",
       "      <td>2.48</td>\n",
       "      <td>28.5892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>75</td>\n",
       "      <td>33</td>\n",
       "      <td>3</td>\n",
       "      <td>2.57</td>\n",
       "      <td>16.4162</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   % variance Explain  no of components  best K used  test error in %  \\\n",
       "0                  99               331            1             3.12   \n",
       "1                  95               155            3             2.78   \n",
       "2                  90                87            3             2.65   \n",
       "3                  85                59            3             2.48   \n",
       "4                  75                33            3             2.57   \n",
       "\n",
       "   query time (ms)  \n",
       "0         123.0881  \n",
       "1          50.6090  \n",
       "2          36.7794  \n",
       "3          28.5892  \n",
       "4          16.4162  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABkkAAANXCAYAAACR8rjpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ae20d314e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "querytimes_ = [round(result_pca[3]/10, 4), round(result_pca_low[3]/10, 4), round(result_pca_low_1[3]/10, 4), round(result_pca_low_2[3]/10, 4), round(result_pca_low_3[3]/10, 4)]\n",
    "var_exp_ = [99, 95, 90, 85, 75]\n",
    "components_ = [331, 155, 87, 59, 33]\n",
    "err_ = [3.12, 2.78, 2.65, 2.48, 2.57]\n",
    "best_k_ = [1, 3, 3, 3, 3]\n",
    "pca_transform_results(err_, var_exp_, components_, best_k_, querytimes_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The immediate table and plot above summarise the result of the PCA transformations by 33, 59, 87, 155 and 331 components which correspond to 75, 85 90, 95 and 99 percent variance explained.\n",
    "\n",
    "The best value of K is 3 except in the transformation with 331 components where K is 1, also the best test error rate is at transformation with 59 components. Transformation with 331 components performs poorly in terms of query time and error rate. \n",
    "\n",
    "Generally, transformation with 59 component(85% variance explained) is efficient in terms of low error rate and low query time, it is by far the best in this study. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}