Journal of Applied Mathematics

An Adaptive Reordered Method for Computing PageRank

Yi-Ming Bu and Ting-Zhu Huang

Full-text: Open access

Abstract

We propose an adaptive reordered method to deal with the PageRank problem. It has been shown that one can reorder the hyperlink matrix of PageRank problem to calculate a reduced system and get the full PageRank vector through forward substitutions. This method can provide a speedup for calculating the PageRank vector. We observe that in the existing reordered method, the cost of the recursively reordering procedure could offset the computational reduction brought by minimizing the dimension of linear system. With this observation, we introduce an adaptive reordered method to accelerate the total calculation, in which we terminate the reordering procedure appropriately instead of reordering to the end. Numerical experiments show the effectiveness of this adaptive reordered method.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 507915, 6 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808074

Digital Object Identifier
doi:10.1155/2013/507915

Mathematical Reviews number (MathSciNet)
MR3082133

Zentralblatt MATH identifier
1311.68020

Citation

Bu, Yi-Ming; Huang, Ting-Zhu. An Adaptive Reordered Method for Computing PageRank. J. Appl. Math. 2013 (2013), Article ID 507915, 6 pages. doi:10.1155/2013/507915. https://projecteuclid.org/euclid.jam/1394808074


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References

  • S. Brin, L. Page, R. Motwami, and T. Winograd, “The PageRank citation ranking:bringing order to the web,” Tech. Rep. 1999-0120, Computer Science Department, Stanford University, Stanford, Calif, USA, 1999.
  • S. Brin and L. Page, “The anatomy of a large-scale hypertextual web search engine,” Computer Networks and ISDN Systems, vol. 30, no. 1–7, pp. 107–117, 1998.
  • S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and G. H. Golub, “Extrapolationmethods for accelerating PageRank computations,” in Proceedings of the 12th International World Wide Web Conference, ACM Press, New York, NY, USA, 2003.
  • S. D. Kamvar, T. H. Haveliwala, and G. H. Golub, “Adaptive methods for the computationof PageRank,” Tech. Rep. 2003-26, Stanford University, Stanford, Calif, USA, 2003.
  • Y. Lin, X. Shi, and Y. Wei, “On computing PageRank via lumping the Google matrix,” Journal of Computational and Applied Mathematics, vol. 224, no. 2, pp. 702–708, 2009.
  • G. Wu and Y. Wei, “A Power-Arnoldi algorithm for computing PageRank,” Numerical Linear Algebra with Applications, vol. 14, no. 7, pp. 521–546, 2007.
  • G. Wu and Y. Wei, “Arnoldi versus GMRES for computing PageRank: a theoreticalcontribution to Google's PageRank problem,” ACM Transactions on Information Systems, vol. 28, no. 3, article 11, 2010.
  • G. Wu and Y. Wei, “An Arnoldi-extrapolation algorithm for computing PageRank,” Journal of Computational and Applied Mathematics, vol. 234, no. 11, pp. 3196–3212, 2010.
  • G. Wu, Y. Zhang, and Y. Wei, “Krylov subspace algorithms for computing GeneRank for the analysis of microarray data mining,” Journal of Computational Biology, vol. 17, no. 4, pp. 631–646, 2010.
  • Q. Yu, Z. Miao, G. Wu, and Y. Wei, “Lumping algorithms for computing Google's PageRank and its derivative, with attention to unreferenced nodes,” Information Retrieval, vol. 15, no. 6, pp. 503–526, 2012.
  • G. Wu, W. Xu, Y. Zhang, and Y. Wei, “A preconditioned conjugate gradient algorithm for GeneRank with application to microarray data mining,” Data Mining and Knowledge Discovery, vol. 26, no. 1, pp. 27–56, 2013.
  • C. P. C. Lee, G. H. Golub, and S. A. Zenios, “A fast two-stagealgorithm for computingPageRank and its extensions,” Tech. Rep. SCCM-2003-15, Scientific Computationand Computational Mathematics, Stanford University, Stanford, CA, USA, 2003.
  • A. N. Langville and C. D. Meyer, “A reordering for the PageRank problem,” SIAM Journal on Scientific Computing, vol. 27, no. 6, pp. 2112–2120, 2006.
  • http://www.cise.ufl.edu/research/sparse/matrices/Gleich/wb- cs-stanford.html.
  • http://www.cise.ufl.edu/research/sparse/matrices/Kamvar/ Stanford.html.