Robust PCA Through Maximum Correntropy Power Iterations

Abstract

Principal component analysis (PCA) is considered a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known lack of robustness of PCA for non-Gaussian data and/or outliers often makes its practical use unreliable. To this end, we introduce a robust formulation of PCA based on the maximum correntropy criterion (MCC). By virtue of MCC, robust operation is achieved by maximising the expected likelihood of Gaussian distributed reconstruction errors. The analysis shows that the proposed solution reduces to a generalised power iteration, whereby: (i) robust estimates of the principal components are obtained even in the presence of outliers; (ii) the number of principal components need not be specified in advance; and (iii) the entire set of principal components can be obtained, unlike existing approaches. The advantages of the proposed maximum correntropy power iteration (MCPI) are demonstrated through an intuitive numerical example.