Sparsity control for robust principal component analysis

Gonzalo Mateos, Georgios B. Giannakis
2010 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers  
Principal component analysis (PCA) is widely used for high-dimensional data analysis, with well-documented applications in computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify PCA against outliers. A least-trimmed squares estimator of a low-rank component analysis model is shown closely related to that obtained from an 0-(pseudo)normregularized criterion
more » ... aging sparsity in a matrix explicitly modeling the outliers. This connection suggests efficient (approximate) solvers based on convex relaxation, which lead naturally to a family of robust estimators subsuming Huber's optimal Mclass. Outliers are identified by tuning a regularization parameter, which amounts to controlling the sparsity of the outlier matrix along the whole robustification path of (group)-Lasso solutions. Novel algorithms are developed to: i) estimate the low-rank data model both robustly and adaptively; and ii) determine principal components robustly in (possibly) infinite-dimensional feature spaces. Numerical tests corroborate the effectiveness of the proposed robust PCA scheme for a video surveillance task. †
doi:10.1109/acssc.2010.5757875 fatcat:pmioyzyvdnfcfmpk4o2yotbwlu