-
Boldi, P.; Santini, M.; Vigna, S.: PageRank as a function of the damping factor (2005)
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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
-
Page, L.; Brin, S.; Motwani, R.; Winograd, T.: ¬The PageRank citation ranking : Bringing order to the Web (1999)
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-
Koch, T.: Searching the Web : systematic overview over indexes (1995)
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-
Koch, T.: Suchmaschinen im Internet (1996)
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-
Stanley, T.: Alta Vista vs. Lycos (1996)
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-
Dunning, A.: Do we still need search engines? (1999)
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- Source
- Ariadne. 1999, no.22
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Koch, T.: Literature about search services (1996)
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-
Birmingham, J.: Internet search engines (1996)
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- Date
- 10.11.1996 16:36:22
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Bryan, K.; Leise, T.: ¬The $25.000.000.000 eigenvector : the linear algebra behind Google
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-
Hughes, T.; Acharya, A.: ¬An interview with Anurag Acharya, Google Scholar lead engineer
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-
Bensman, S.J.: Eugene Garfield, Francis Narin, and PageRank : the theoretical bases of the Google search engine (2013)
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- Date
- 17.12.2013 11:02:22
-
Ding, L.; Finin, T.; Joshi, A.; Peng, Y.; Cost, R.S.; Sachs, J.; Pan, R.; Reddivari, P.; Doshi, V.: Swoogle : a Semantic Web search and metadata engine (2004)
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Baeza-Yates, R.; Boldi, P.; Castillo, C.: Generalizing PageRank : damping functions for linkbased ranking algorithms (2006)
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- Date
- 16. 1.2016 10:22:28
-
Maurer, H.; Balke, T.; Kappe,, F.; Kulathuramaiyer, N.; Weber, S.; Zaka, B.: Report on dangers and opportunities posed by large search engines, particularly Google (2007)
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