Using Polynomial Chaos to Compute the Influence of Multiple Random Surfers in the PageRank Model

  • Paul G. Constantine
  • David F. Gleich
Conference paper

DOI: 10.1007/978-3-540-77004-6_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4863)
Cite this paper as:
Constantine P.G., Gleich D.F. (2007) Using Polynomial Chaos to Compute the Influence of Multiple Random Surfers in the PageRank Model. In: Bonato A., Chung F.R.K. (eds) Algorithms and Models for the Web-Graph. WAW 2007. Lecture Notes in Computer Science, vol 4863. Springer, Berlin, Heidelberg

Abstract

The PageRank equation computes the importance of pages in a web graph relative to a single random surfer with a constant teleportation coefficient. To be globally relevant, the teleportation coefficient should account for the influence of all users. Therefore, we correct the PageRank formulation by modeling the teleportation coefficient as a random variable distributed according to user behavior. With this correction, the PageRank values themselves become random. We present two methods to quantify the uncertainty in the random PageRank: a Monte Carlo sampling algorithm and an algorithm based the truncated polynomial chaos expansion of the random quantities. With each of these methods, we compute the expectation and standard deviation of the PageRanks. Our statistical analysis shows that the standard deviation of the PageRanks are uncorrelated with the PageRank vector.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Paul G. Constantine
    • 1
  • David F. Gleich
    • 1
  1. 1.Stanford University, Institute for Computational and Mathematical Engineering 

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