Less is more: Compact matrix decomposition for large sparse graphs

Jimeng Sun, Yinglian Xie, Hui Zhang, Christos Faloutsos

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Given a large sparse graph, how can we find patterns and anomalies? Several important applications can be modeled as large sparse graphs, e.g., network traffic monitoring, research citation network analysis, social network analysis, and regulatory networks in genes. Low rank decompositions, such as SVD and CUR, are powerful techniques for revealing latentlhidden variables and associated patterns from high dimensional data. However, those methods often ignore the sparsity property of the graph, and hence usually incur too high memory and computational cost to be practical. We propose a novel method, the Compact Matrix Decomposition (CMD), to compute sparse low rank approximations. CMD dramatically reduces both the computation cost and the space requirements over existing decomposition methods (SVD, CUR). Using CMD as the key building block, we further propose procedures to efficiently construct and analyze dynamic graphs from real-time application data. We provide theoretical guarantee for our methods, and present results on two real, large datasets, one on network flow data (100GB trace of 22K hosts over one month) and one on DBLP (200MB over 25 years). We show that CMD is often an order of magnitude more efficient than the state of the art (SVD and CUR): it is over 1 OX faster, but requires less than 1/10 of the space, for the same reconstruction accuracy. Finally, we demonstrate how CMD is used for detecting anomalies and monitoring time-evolving graphs, in which it successfully detects worm-like hierarchical scanning patterns in real network data.

Original languageEnglish (US)
Title of host publicationProceedings of the 7th SIAM International Conference on Data Mining
PublisherSociety for Industrial and Applied Mathematics Publications
Number of pages12
ISBN (Print)9780898716306
StatePublished - Dec 1 2007
Externally publishedYes
Event7th SIAM International Conference on Data Mining - Minneapolis, MN, United States
Duration: Apr 26 2007Apr 28 2007

Publication series

NameProceedings of the 7th SIAM International Conference on Data Mining


Other7th SIAM International Conference on Data Mining
Country/TerritoryUnited States
CityMinneapolis, MN

ASJC Scopus subject areas

  • Engineering(all)


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