Robust Principal Component Analysis Based on Globally-convergent Iteratively Reweighted Least Squares

Abstract

Classical Robust Principal Component Analysis (RPCA) uses the singular value threshold operator (SVT) to solve for the convex approximation of the nuclear norm with respect to the rank of a matrix. However, when the matrix size is large, the SVT operator has a slow convergent speed and high computational complexity. To solve the above problems, in this paper, we propose a Robust principal component analysis algorithm based on Global-convergent Iteratively Reweighted Least Squares (RPCA/GIRLS). In the first stage, the low-rank matrix in the original RPCA model is decomposed into two column-sparse matrix factor products, and the two matrix factors are solved via alternating iteratively reweighted least squares algorithms (AIRLS), thus reducing the computational complexity. However, since the AIRLS is sensitive to the initialization, the updated matrix factor in the first stage is used as the new input data matrix in the second stage, and the matrix factor is updated by the gradient descent step, and finally the optimal low-rank matrix that satisfies the global convergent conditions is obtained. We have conducted extensive experiments on six public video data sets, by comparing the background separation effects of these six videos and calculating their quantitative evaluation indexes, the effectiveness and superiority of the proposed algorithm are verified from both subjective and objective perspectives.