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Abstract

PageRank is defined as the stationary state of a Markov chain. The chain is obtained by perturbing the transition matrix induced by a web graph with a damping factor alpha that spreads uniformly part of the rank. The choice of alpha is eminently empirical, and in most cases the original suggestion alpha=0.85 by Brin and Page is still used. Recently, however, the behaviour of PageRank with respect to changes in alpha was discovered to be useful in link-spam detection. Moreover, an analytical justification of the value chosen for alpha is still missing. In this paper, we give the first mathematical analysis of PageRank when alpha changes. In particular, we show that, contrarily to popular belief, for real-world graphs values of alpha close to 1 do not give a more meaningful ranking. Then, we give closed-form formulae for PageRank derivatives of any order, and an extension of the Power Method that approximates them with convergence O(t**k*alpha**t) for the k-th derivative. Finally, we show a tight connection between iterated computation and analytical behaviour by proving that the k-th iteration of the Power Method gives exactly the PageRank value obtained using a Maclaurin polynomial of degree k. The latter result paves the way towards the application of analytical methods to the study of PageRank.

Date

16. 1.2016 10:22:28

Source

http://vigna.di.unimi.it/ftp/papers/PageRankAsFunction.pdf [Proceedings of the ACM World Wide Web Conference (WWW), 2005]

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Abstract

The goal of the study presented in this article is to investigate to what extent the classification of a web page by a single genre matches the users' perspective. The extent of agreement on a single genre label for a web page can help understand whether there is a need for a different classification scheme that overrides the single-genre labelling. My hypothesis is that a single genre label does not account for the users' perspective. In order to test this hypothesis, I submitted a restricted number of web pages (25 web pages) to a large number of web users (135 subjects) asking them to assign only a single genre label to each of the web pages. Users could choose from a list of 21 genre labels, or select one of the two 'escape' options, i.e. 'Add a label' and 'I don't know'. The rationale was to observe the level of agreement on a single genre label per web page, and draw some conclusions about the appropriateness of limiting the assignment to only a single label when doing genre classification of web pages. Results show that users largely disagree on the label to be assigned to a web page.