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THE POWER METHOD FOR THE PAGERANK VECTOR 3
"... P ̃ is the stochastic reducible matrix, without dangling nodes, related to the Google matrix P ∈ Rp×p. Pc = cP̃+ (1 − c)E is a stochastic and irreducible matrix where c ∈ [0,1),E = evT, e = (1,...,1)T and v = e/p. As we saw, the power method r(n+1)c = P T c r ..."
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P ̃ is the stochastic reducible matrix, without dangling nodes, related to the Google matrix P ∈ Rp×p. Pc = cP̃+ (1 − c)E is a stochastic and irreducible matrix where c ∈ [0,1),E = evT, e = (1,...,1)T and v = e/p. As we saw, the power method r(n+1)c = P T c r
TopicSensitive PageRank
, 2002
"... In the original PageRank algorithm for improving the ranking of searchquery results, a single PageRank vector is computed, using the link structure of the Web, to capture the relative "importance" of Web pages, independent of any particular search query. To yield more accurate search resu ..."
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Cited by 532 (10 self)
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In the original PageRank algorithm for improving the ranking of searchquery results, a single PageRank vector is computed, using the link structure of the Web, to capture the relative "importance" of Web pages, independent of any particular search query. To yield more accurate search
Article electronically published on February 7, 2008 RATIONAL EXTRAPOLATION FOR THE PAGERANK VECTOR
"... Abstract. An important problem in web search is to determine the importance of each page. From the mathematical point of view, this problem consists in finding the nonnegative left eigenvector of a matrix corresponding to its dominant eigenvalue 1. Since this matrix is neither stochastic nor irreduc ..."
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irreducible, the power method has convergence problems. So, the matrix is replaced by a convex combination, depending on a parameter c, with a rank one matrix. Its left principal eigenvector now depends on c, and it is the PageRank vector we are looking for. However, when c is close to 1, the problem is ill
Scaling Personalized Web Search
 In Proceedings of the Twelfth International World Wide Web Conference
, 2002
"... Recent web search techniques augment traditional text matching with a global notion of "importance" based on the linkage structure of the web, such as in Google's PageRank algorithm. For more refined searches, this global notion of importance can be specialized to create personalized ..."
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Cited by 404 (2 self)
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Recent web search techniques augment traditional text matching with a global notion of "importance" based on the linkage structure of the web, such as in Google's PageRank algorithm. For more refined searches, this global notion of importance can be specialized to create personalized
Topicsensitive pagerank: A contextsensitive ranking algorithm for web search
 IEEE Transactions on Knowledge and Data Engineering
, 2003
"... Abstract—The original PageRank algorithm for improving the ranking of searchquery results computes a single vector, using the link structure of the Web, to capture the relative “importance ” of Web pages, independent of any particular search query. To yield more accurate search results, we propose ..."
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Cited by 230 (2 self)
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Abstract—The original PageRank algorithm for improving the ranking of searchquery results computes a single vector, using the link structure of the Web, to capture the relative “importance ” of Web pages, independent of any particular search query. To yield more accurate search results, we propose
A survey on pagerank computing
 Internet Mathematics
, 2005
"... Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. T ..."
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Cited by 104 (0 self)
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Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component
Exploiting the Block Structure of the Web for Computing PageRank
, 2003
"... The web link graph has a nested block structure: the vast majority of hyperlinks link pages on a host to other pages on the same host, and many of those that do not link pages within the same domain. We show how to exploit this structure to speed up the computation of PageRank by a 3stage alg ..."
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Cited by 158 (4 self)
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starting vector the weighted concatenation of the local PageRanks. Empirically, this algorithm speeds up the computation of PageRank by a factor of 2 in realistic scenarios. Further, we develop a variant of this algorithm that efficiently computes many different "personalized" PageRanks
An Application of Personalized PageRank Vectors: Personalized Search Engine
"... Abstract. We introduce a tool which is an application of personalized pagerank vectors such as personalized search engines. We use precomputed pagerank vectors to rank the search results in favor of user preferences. We describe the design and architecture of our tool. By using precomputed persona ..."
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Abstract. We introduce a tool which is an application of personalized pagerank vectors such as personalized search engines. We use precomputed pagerank vectors to rank the search results in favor of user preferences. We describe the design and architecture of our tool. By using pre
MULTILINEAR PAGERANK∗
"... Abstract. In this paper, we first extend the celebrated PageRank modification to a higherorder Markov chain. Although this system has attractive theoretical properties, it is computationally intractable for many interesting problems. We next study a computationally tractable approximation to the hi ..."
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to the higherorder PageRank vector that involves a system of polynomial equations called multilinear PageRank. This is motivated by a novel “spacey random surfer ” model, where the surfer remembers bits and pieces of history and is influenced by this information. The underlying stochastic process
Dynamic Personalized Pagerank in EntityRelation Graphs
, 2007
"... Extractors and taggers turn unstructured text into entityrelation (ER) graphs where nodes are entities (email, paper, person, conference, company) and edges are relations (wrote, cited, worksfor). Typed proximity search of the form type=person NEAR company∼"IBM", paper∼"X ..."
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Cited by 81 (3 self)
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” subgraph is identified, bordered by nodes with indexed fingerprints. These fingerprints are adaptively loaded to various resolutions to form approximate personalized Pagerank vectors (PPVs). PPVs at remaining active nodes are now computed iteratively. We report on experiments with CiteSeer’s ER graph
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