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ASAP : Towards Accurate, Stable and Accelerative Penetrating-Rank Estimation on Large Graphs

  • Xuefei Li
  • Weiren Yu
  • Bo Yang
  • Jiajin Le
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6897)

Abstract

Pervasive web applications increasingly require a measure of similarity among objects. Penetrating-Rank (P-Rank) has been one of the promising link-based similarity metrics as it provides a comprehensive way of jointly encoding both incoming and outgoing links into computation for emerging applications. In this paper, we investigate P-Rank efficiency problem that encompasses its accuracy, stability and computational time. (1) We provide an accuracy estimate for iteratively computing P-Rank. A symmetric problem is to find the iteration number K needed for achieving a given accuracy ε. (2) We also analyze the stability of P-Rank, by showing that small choices of the damping factors would make P-Rank more stable and well-conditioned. (3) For undirected graphs, we also explicitly characterize the P-Rank solution in terms of matrices. This results in a novel non-iterative algorithm, termed ASAP , for efficiently computing P-Rank, which improves the CPU time from O(n 4) to O( n 3 ). Using real and synthetic data, we empirically verify the effectiveness and efficiency of our approaches.

Keywords

Weighting Factor Synthetic Data Undirected Graph Undirected Network Conditional Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xuefei Li
    • 1
  • Weiren Yu
    • 2
    • 3
  • Bo Yang
    • 3
  • Jiajin Le
    • 3
  1. 1.Fudan UniversityChina
  2. 2.University of New South Wales & NICTAAustralia
  3. 3.Donghua UniversityChina

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