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Asymptotic Analysis for Personalized Web Search Yana Volkovich and Nelly Litvak
 

Summary: Asymptotic Analysis for Personalized Web Search
Yana Volkovich and Nelly Litvak
Department of Applied Mathematics, University of Twente
PO Box 217, 7500 AE Enschede, The Netherlands
e-mail:{y.volkovich, n.litvak}@ewi.utwente.nl
Abstract
Personalized PageRank is used in Web search as an importance mea-
sure for Web documents. The goal of this paper is to characterize the
tail behavior of the PageRank distribution in the Web and other complex
networks characterized by power laws. To this end, we model the Page-
Rank as a solution of a stochastic equation R
d
= N
i=1 AiRi + B, where
Ri's are distributed as R. This equation is inspired by the original defi-
nition of the PageRank. In particular, N models the number of incoming
links of a page, and B stays for the user preference. Assuming that N
or B are heavy-tailed, we employ the theory of regular variation to ob-
tain the asymptotic behavior of R under quite general assumptions on
the involved random variables. Our theoretical predictions show a good

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering