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Anomalous subgraph detection via Sparse Principal Component Analysis

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4 Author(s)
Singh, N. ; Dept. of Electr. Eng., Stanford Univ., Stanford, CA, USA ; Miller, B.A. ; Bliss, N.T. ; Wolfe, P.J.

Network datasets have become ubiquitous in many fields of study in recent years. In this paper we investigate a problem with applicability to a wide variety of domains - detecting small, anomalous subgraphs in a background graph. We characterize the anomaly in a subgraph via the well-known notion of network modularity, and we show that the optimization problem formulation resulting from our setup is very similar to a recently introduced technique in statistics called Sparse Principal Component Analysis (Sparse PCA), which is an extension of the classical PCA algorithm. The exact version of our problem formulation is a hard combinatorial optimization problem, so we consider a recently introduced semidefinite programming relaxation of the Sparse PCA problem. We show via results on simulated data that the technique is very promising.

Published in:

Statistical Signal Processing Workshop (SSP), 2011 IEEE

Date of Conference:

28-30 June 2011