Citation Weighted Page Rank
PageRank was initially developed by Page et.al.[1] in 1999. Ding et.al. propose a framework to modify PageRank to add a weight component[2]. The intrinsic nature of PageRank accounts for collaboration due to the underlying Markov chain. But to account for the individual contribution of an author we weigh the algorithm proportional to the total citations. The weighted PageRank of an author ai is defined as follows.
- Initialize W to a square matrix of size N where N is the number of authors. Each cell in the matrix represents the collaboration between authors. For example Wij represents the collaboration between author i and author j.
- Initialize PR to a a square matrix of size N as well using a uniform random distribution between 0 and 1.
- For each randomly select an author and update PR(ai)using the following equation.
where θ is the probability of collaboration set between 0 and 1. A high value of θ leads to more faster convergence but can result in instability while a low value leads to slower convergence. W(ai) represents the weight associated with an author in this case we use the number of citations as the weight. W(ai) represents the collaborators of an author ai. For our experiments, we use θ = 0.4.
Comparing against other measures:
- Infl: Total citations of the authors.
- CoA: Total number of co-authored articles.
- Frac: Represents the fractional credit per co-author which is the cumulative citation count for each article weighted by the unit fractional credit. Unit fractional credit is the contribution of an author towards an article defined as the reciprocal of number coauthors in an article.
- Harm: Represents the harmonic credit per co-author which is the cumulative citation count for each article weighted by the unit harmonic credit based on the co-author's position.
[1] L. Page, S. Brin, R. Motwani, and T. Winograd, "The pagerank citation ranking: order to the web." Stanford InfoLab, Tech. Rep., 1999.
[2] Y. Ding, E. Yan, A. Frazho, and J. Caverlee, "Pagerank for ranking authors in co-citation networks." Journal of the American Society for Information Science andTechnology, vol. 60, no. 11, pp. 2229–2243, 2009.