Fast R in addition to om Walk with Restart in addition to Its Applications Motivating Questions R in addition to om walk with restart R in addition to om walk with restart Automatic Image Caption

Fast R in addition to om Walk with Restart in addition to Its Applications Motivating Questions R in addition to om walk with restart R in addition to om walk with restart Automatic Image Caption www.phwiki.com

Fast R in addition to om Walk with Restart in addition to Its Applications Motivating Questions R in addition to om walk with restart R in addition to om walk with restart Automatic Image Caption

Lanier-Graham, Susan, Freelance Writer has reference to this Academic Journal, PHwiki organized this Journal Fast R in addition to om Walk with Restart in addition to Its Applications Hanghang Tong, Christos Faloutsos in addition to Jia-Yu (Tim) Pan ICDM 2006 Dec. 18-22, HongKong Motivating Questions Q: How to measure the relevance A: R in addition to om walk with restart Q: How to do it efficiently A: This talk tries to answer! R in addition to om walk with restart

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R in addition to om walk with restart Ranking vector More red, more relevant Nearby nodes, higher scores Automatic Image Caption Q Sea Sun Sky Wave { } A: RWR! [Pan KDD2004] Test Image Image Keyword Region

Test Image Sea Sun Sky Wave Cat Forest Tiger Grass Image Keyword Region {Grass, Forest, Cat, Tiger} Neighborhood Formulation Conference Author A: RWR! [Sun ICDM2005] Q: what is most related conference to ICDM NF: example

Center-Piece Subgraph(CePS) Original Graph Black: query nodes CePS Q A: RWR! [Tong KDD 2006] CePS: Example Other Applications Content-based Image Retrieval [He] Personalized PageRank [Jeh], [Widom], [Haveliwala] Anomaly Detection ( as long as node; link) [Sun] Link Prediction [Getoor], [Jensen] Semi-supervised Learning [Zhu], [Zhou]

Roadmap Background RWR: Definitions RWR: Algorithms Basic Idea FastRWR Pre-Compute Stage On-Line Stage Experimental Results Conclusion Computing RWR n x n n x 1 n x 1 Ranking vector Starting vector Adjacent matrix 1 Restart p Beyond RWR P-PageRank [Haveliwala] PageRank [Haveliwala] RWR [Pan, Sun] SM Learning [Zhou, Zhu] RL in CBIR [He] Fast RWR Finds the Root Solution ! : Maxwell Equation as long as Web! [Chakrabarti]

Q: Given query i, how to solve it OntheFly: No pre-computation/ light storage Slow on-line response O(mE) PreCompute 4 1 3 2 5 6 7 9 10 8 11 12 [Haveliwala] R:

PreCompute: Fast on-line response Heavy pre-computation/storage cost O(n ) O(n ) 3 2 Q: How to Balance On-line Off-line Roadmap Background RWR: Definitions RWR: Algorithms Basic Idea FastRWR Pre-Compute Stage On-Line Stage Experimental Results Conclusion

Basic Idea Find Community Fix the remaining Combine Pre-computational stage Q: A: A few small, instead of ONE BIG, matrices inversions Efficiently compute in addition to store Q -1 On-Line Query Stage Q: Efficiently recover one column of Q A: A few, instead of MANY, matrix-vector multiplication + -1

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Roadmap Background RWR: Definitions RWR: Algorithms Basic Idea FastRWR Pre-Compute Stage On-Line Stage Experimental Results Conclusion Pre-compute Stage p1: B-Lin Decomposition P1.1 partition P1.2 low-rank approximation p2: Q matrices P2.1 computing ( as long as each partition) P2.2 computing ( as long as concept space) P1.1: partition 1 4 3 2 5 6 7 9 10 8 11 12 Within-partition links cross-partition links

P1.1: block-diagonal 1 4 3 2 5 6 7 9 10 8 11 12 P1.2: LRA as long as 3 1 4 2 5 6 7 9 10 8 11 12 S W2 ~ + =

Q&A Thank you! htong@cs.cmu.edu www.cs.cmu.edu/~htong

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