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Extrapolation and minimization procedures for the PageRank vector

Authors: Claude Brezinski and Michela Redivo-Zaglia

Published in: Dagstuhl Seminar Proceedings, Volume 7071, Web Information Retrieval and Linear Algebra Algorithms (2007)

Abstract

An important problem in Web search is to determine the importance of each page. This problem consists in computing, by the power method, the left principal eigenvector (the PageRank vector) of a matrix depending on a parameter $c$ which has to be chosen close to 1. However, when $c$ is close to 1, the problem is ill-conditioned, and the power method converges slowly. So, the idea developed in this paper consists in computing the PageRank vector for several values of $c$, and then to extrapolate them, by a conveniently chosen rational function, at a point near 1. The choice of this extrapolating function is based on the mathematical considerations about the PageRank vector.

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Claude Brezinski and Michela Redivo-Zaglia. Extrapolation and minimization procedures for the PageRank vector. In Web Information Retrieval and Linear Algebra Algorithms. Dagstuhl Seminar Proceedings, Volume 7071, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brezinski_et_al:DagSemProc.07071.9,
  author =	{Brezinski, Claude and Redivo-Zaglia, Michela},
  title =	{{Extrapolation and minimization procedures for the PageRank vector}},
  booktitle =	{Web Information Retrieval and Linear Algebra Algorithms},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7071},
  editor =	{Andreas Frommer and Michael W. Mahoney and Daniel B. Szyld},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07071.9},
  URN =		{urn:nbn:de:0030-drops-10682},
  doi =		{10.4230/DagSemProc.07071.9},
  annote =	{Keywords: Extrapolation, PageRank, Web matrix, eigenvector computation.}
}

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Extrapolation and minimization procedures for the PageRank vector

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