Less is More: Compact Matrix Decomposition for Large Sparse Graphs

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 latent/hidden 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 guaran...

• Type: Conference
• Year: 2007
• Where: SDM
• Authors: Jimeng Sun, Yinglian Xie, Hui Zhang, Christos Faloutsos
• Keywords: Data Mining, Large Sparse Graphs, Low Rank, Network Analysis, SDM 2007