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Random Walk with Restart: Anomaly Detection and Its Applications

This presentation explores the Random Walk with Restart (RWR) algorithm and its applications in anomaly detection. By calculating relevance scores for nodes based on neighborhood formation and transition probability, we can identify anomalies in networks. This method allows for on-the-fly analysis without extensive pre-computation, providing quick responses and significant improvements in detection quality. The RWR algorithm is demonstrated on a large dataset containing 315K nodes and 1.8M edges.

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Random Walk with Restart: Anomaly Detection and Its Applications

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  1. 10-831 Event and Pattern Detection Topic Presentation - IIFAST RANDOM WALK WITH RESTARTand its applicationsHanghang Tong, Christos Faloutsos, Jia-Yu (Tim) PanICDM 2006 Leman Akoglu lakoglu@cs.cmu.edu February 2010

  2. .3 .2 .05 .01 .002 .01 Random Walk with Restart • Neighborhood formation • Given a node q, what are the relevance scores of all the nodes to q? V1 V2 q

  3. RWR for Anomaly Detection t t high normality low normality • Anomaly detection (AD) • Given a node q, what are the normality scores for nodes that link to q?

  4. RWR algebra: Steady-state probability vector (relevance scores) Starting vector Transition matrix Restart probability ? ?

  5. 10 9 12 2 8 1 11 3 0.04 0.03 10 9 0.10 12 4 0.13 0.08 2 0.02 8 1 11 0.13 3 6 0.04 5 4 0.05 6 5 0.13 7 7 0.05 OntheFly: No pre-computation/ light storage Slow on-line response O(mE)

  6. 0.04 0.03 10 9 0.10 12 0.13 0.08 2 0.02 8 1 11 0.13 3 0.04 4 0.05 6 5 0.13 7 0.05 PreCompute 10 9 12 2 8 1 11 R: 3 4 6 5 7 [Haveliwala]

  7. 10 9 12 2 8 1 11 3 0.04 0.03 10 9 0.10 12 4 0.13 0.08 2 0.02 8 1 11 0.13 3 6 0.04 5 4 0.05 6 5 0.13 7 7 0.05 PreCompute: Fast on-line response Heavy pre-computation/storage cost O(n ) 3 O(n ) 2

  8. Sherman–Morrison–Woodbury Lemma says: • Can we write as (A+UCV) • for which • P1: A is easy to invert, and • P2: C is small?

  9. 10 9 12 2 8 1 11 3 4 6 5 7 Intiution 10 9 12 2 8 1 11 3 4 6 5 7 Within-partition links cross-partition links

  10. 10 9 12 2 8 1 11 3 4 6 5 7 P1: block-diagonal 10 9 12 2 8 1 11 3 4 6 5 7

  11. 10 9 12 2 8 1 11 3 4 6 5 7 P2: Low-Rank-Approx. for 10 9 12 2 8 1 11 3 4 6 5 7 ~ |S| <<|W2|

  12. = +

  13. Is easily convertible? YES! A few small, instead of ONE BIG, matrix inversions

  14. Back to SM Lemma + ? ~ + ~

  15. On-Line Stage: A handful of Matrix-Vector mult.s ? + Query Result Pre-Computation

  16. Query Time vs. Pre-Storage • Quality: 90%+ • On-line: • Up to 150x speedup • Pre-storage: • 3orders saving Log Query Time • Dataset • DBLP/authorship • 315k nodes • 1,800k edges Log Storage

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