Fast incremental proximity search in large graphs

In this paper we investigate two aspects of ranking problems on large graphs. First, we augment the deterministic pruning algorithm in Sarkar and Moore (2007) with sampling techniques to compute approximately correct rankings with high probability under random walk based proximity measures at query time. Second, we prove some surprising locality properties of these proximity measures by examining the short term behavior of random walks. The proposed algorithm can answer queries on the fly without caching any information about the entire graph. We present empirical results on a 600, 000 node author-word-citation graph from the Citeseer domain on a single CPU machine where the average query processing time is around 4 seconds. We present quantifiable link prediction tasks. On most of them our techniques outperform Personalized Pagerank, a well-known diffusion based proximity measure.

[1]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[2]  D. Aldous,et al.  Chapter 3 Reversible Markov Chains , 1994 .

[3]  Taher H. Haveliwala.  Topic-sensitive PageRank , 2002, IEEE Trans. Knowl. Data Eng..

[4]  Jennifer Widom,et al.  SimRank: a measure of structural-context similarity , 2002, KDD.

[5]  Jon Kleinberg,et al.  The link prediction problem for social networks , 2003, CIKM '03.

[6]  Jennifer Widom,et al.  Scaling personalized web search , 2003, WWW '03.

[7]  Dániel Fogaras,et al.  Towards Scaling Fully Personalized PageRank , 2004, WAW.

[8]  Vagelis Hristidis,et al.  ObjectRank: Authority-Based Keyword Search in Databases , 2004, VLDB.

[9]  Dániel Fogaras,et al.  Towards Scaling Fully Personalized PageRank: Algorithms, Lower Bounds, and Experiments , 2005, Internet Math..

[10]  Matthew Brand,et al.  A Random Walks Perspective on Maximizing Satisfaction and Profit , 2005, SDM.

[11]  Soumen Chakrabarti,et al.  Dynamic personalized pagerank in entity-relation graphs , 2007, WWW '07.

[12]  Jon M. Kleinberg,et al.  The link-prediction problem for social networks , 2007, J. Assoc. Inf. Sci. Technol..

[13]  Purnamrita Sarkar,et al.  A Tractable Approach to Finding Closest Truncated-commute-time Neighbors in Large Graphs , 2007, UAI.

[14]  David Liben-Nowell,et al.  The link-prediction problem for social networks , 2007 .

[15]  Christos Faloutsos,et al.  Fast direction-aware proximity for graph mining , 2007, KDD '07.

[16]  Nikhil Srivastava,et al.  Graph sparsification by effective resistances , 2008, SIAM J. Comput..