Robust Principal Component Analysis Based On Maximum Correntropy Power Iterations

TL;DR

This paper introduces a robust PCA method based on maximum correntropy power iteration that effectively handles outliers and does not require prior knowledge of the number of principal components.

Contribution

It proposes a novel MCC-based PCA formulation that provides robust estimates, automatically determines the number of components, and retrieves the entire principal component set.

Findings

Robust PCA estimates are obtained even with outliers.

The method does not require pre-specifying the number of components.

The entire set of principal components can be recovered.

Abstract

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust formulation of PCA is derived based on the maximum correntropy criterion (MCC) so as to maximise the expected likelihood of Gaussian distributed reconstruction errors. In this way, 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.