Fast Random Walk with Restart and Its Applications

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 ShermanMorrison lemma for matrix inversion. Experimental results on the Corel ...

• Type: Conference
• Year: 2006
• Where: ICDM
• Authors: Hanghang Tong, Christos Faloutsos, Jia-Yu Pan
• Keywords: Data Mining, ICDM 2006, Low-rank Matrix Approximation, Real Graphs, Straightforward Implementations