Fast random walk with restart and its applications

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Fast random walk with restart and its applications (2006)

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by Hanghang Tong

Venue:	In ICDM ’06: Proceedings of the 6th IEEE International Conference on Data Mining
Citations:	179 - 19 self

BibTeX

@INPROCEEDINGS{Tong06fastrandom,
    author = {Hanghang Tong},
    title = {Fast random walk with restart and its applications},
    booktitle = {In ICDM ’06: Proceedings of the 6th IEEE International Conference on Data Mining},
    year = {2006},
    pages = {613--622},
    publisher = {IEEE Computer Society}
}

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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. 1

Keyphrases

fast random walk straightforward implementation storage cost quality preservation many real graph good relevance score automatic captioning dblp dabasets community structure cubic pre-computation time corel image important property response time low-rank matrix approximation graph partitioning several order real graph random walk numerous setting quadratic space large graph fast solution matrix inversion community-like structure significant saving weighted graph sherman-morrison lemma linear correlation experimental result connection subgraphs

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