Side Information in Robust Principal Component Analysis: Algorithms and Applications

Abstract: Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA has been shown to be very successful in solving many rank minimisation problems, there are still cases where degenerate or suboptimal solutions are obtained. This is likely to be remedied by taking into account of domain-dependent prior knowledge. In this paper, we propose two models for the RPCA problem with the aid of side information on the low-rank structure of the data. The versatility of the proposed methods is demonstrated by applying them to four applications, namely background subtraction, facial image denoising, face and facial expression recognition. Experimental results on synthetic and five real world datasets indicate the robustness and effectiveness of the proposed methods on these application domains, largely outperforming six previous approaches.