Fast random walk with restart and its applications

Hanghang Tong, Christos Faloutsos, Jia Yu Pan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

550 Scopus citations

Abstract

How closely related are two nodes in a graph? How to compute this score quickly, on huge, disk-resident, real graphs? Random walk with restart (RWR) provides a good relevance score between two nodes in a weighted graph, and it has been successfully used in numerous settings, like automatic captioning of images, generalizations to the "connection subgraphs", personalized PageRank, and many more. However, the straightforward implementations of RWR do not scale for large graphs, requiring either quadratic space and cubic pre-computation time, or slow response time on queries. We propose fast solutions to this problem. The heart of our approach is to exploit two important properties shared by many real graphs: (a) linear correlations and (b) blockwise, community-like structure. We exploit the linearity by using low-rank matrix approximation, and the community structure by graph partitioning, followed by the Sherman-Morrison lemma for matrix inversion. Experimental results on the Corel image and the DBLP dabasets demonstrate that our proposed methods achieve significant savings over the straightforward implementations: they can save several orders of magnitude in pre-computation and storage cost, and they achieve up to 150x speed up with 90%+ quality preservation.

Original languageEnglish (US)
Title of host publicationProceedings - Sixth International Conference on Data Mining, ICDM 2006
Pages613-622
Number of pages10
DOIs
StatePublished - Dec 1 2006
Event6th International Conference on Data Mining, ICDM 2006 - Hong Kong, China
Duration: Dec 18 2006Dec 22 2006

Publication series

NameProceedings - IEEE International Conference on Data Mining, ICDM
ISSN (Print)1550-4786

Other

Other6th International Conference on Data Mining, ICDM 2006
CountryChina
CityHong Kong
Period12/18/0612/22/06

ASJC Scopus subject areas

  • Engineering(all)

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    Tong, H., Faloutsos, C., & Pan, J. Y. (2006). Fast random walk with restart and its applications. In Proceedings - Sixth International Conference on Data Mining, ICDM 2006 (pp. 613-622). [4053087] (Proceedings - IEEE International Conference on Data Mining, ICDM). https://doi.org/10.1109/ICDM.2006.70