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A Variational Approach for Sparse Component Estimation and Low-Rank Matrix Recovery

Zhaofu Chen1, Rafael Molina2, and Aggelos K. Katsaggelos1
1.Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, 60208, USA
2.Deptartmento de Ciencias de la Computaci´on e I. A., Universidad de Granada, 18071 Granada, Spain
Abstract—We propose a variational Bayesian based algorithmfor the estimation of the sparse component of an outlier-corrupted low-rank matrix, when linearly transformed compositedata are observed. The model constitutes a generalization ofrobust principal component analysis. The problem consideredherein is applicable in various practical scenarios, such asforeground detection in blurred and noisy video sequences anddetection of network anomalies among others. The proposedalgorithm models the low-rank matrix and the sparse compo-nent using a hierarchical Bayesian framework, and employsa variational approach for inference of the unknowns. Theeffectiveness of the proposed algorithm is demonstrated usingreal life experiments, and its performance improvement overregularization based approaches is shown.
 
Index Terms—Bayesian inference, variational approach, robustprincipal component analysis, foreground detection, networkanomaly detection

Cite: Zhaofu Chen, Rafael Molina, and Aggelos K. Katsaggelos, "A Variational Approach for Sparse Component Estimation and Low-Rank Matrix Recovery," Journal of Communications, vol. 8, no. 9, pp. 600-611, 2013. doi: 10.12720/jcm.8.9.600-611
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