Side Information in Robust Principle Component Analysis: Algorithms and Applications

Niannan Xue, Yannis Panagakis, Stefanos Zafeiriou

Published 2017-02-02Version 1

Robust rank minimisation 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. The most prominent method for this task is the Robust Principal Component Analysis (PCA). It recovers a low-rank matrix from sparse corruptions of unknown magnitude and support by Principal Component Pursuit (PCP), which is a convex approximation to the otherwise NP-hard rank minimisation problem. Even though PCP has been shown to be very successful in solving many rank minimisation problems, there are cases where degenerate or suboptimal solutions are obtained. This can be attributed to the fact that domain-dependent prior knowledge is not taken into account by PCP. In this paper, we address the problem of PCP when prior information is available. To this end, we propose algorithms for solving the PCP problem with the aid of prior 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 substraction, 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 previous approaches that incorporate side information within Robust PCA.