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.

Low Rank Regularization: A Review

“…Here, the low rank matrix Z can be seen as a rough similarity matrix, and the final partitioning result can be obtained by conducting spectral clustering with a refined similarity matrix. Face Analysis [59,[71][72][73] X * ADMM Person Re-Identification [74] X * others Visual Tracking [19,75] X * others 3D Reconstruction [20][21][22][23] X * ADMM Image denoising [30,[76][77][78] k i=1 wiσi ADMM Structure Recovery [79] r i=1 wiσi others Video Desnowing and Deraining [80] X * AM Salient Object Detection [24][25][26][27] X * ADMM Face Recognition [81][82][83] X * ADMM High Dynamic Range Imaging [53,84] X * , r i=k+1 σi ADMM Head Pose Estimation [85] X * ADMM Moving Object Detection [86] X * ADMM Reflection Removal [87] X * others Zero-Shot Learning [88] k i=r+1 σi others Speckle removal [89] k i=r+1 wiσi ADMM Image Completion [90] [93][94][95][96] X| * ADMM Image Restoration [97] X| * ADMM Image Classification [98][99][100][101][102][103] X * ADMM AAM fitting…”

Informed Non-Convex Robust Principal Component Analysis With Features

“…For fast RPCA and our algorithm, a sparsity of 0.2 is adopted. We learn the feature dictionary as in (Xue, Panagakis, and Zafeiriou 2017). In a nutshell, the feature learning process can be treated as a sparse encoding problem.…”

Informed Non-convex Robust Principal Component Analysis with Features

“…For fast RPCA and our algorithm, a sparsity of 0.2 is adopted. We learn the feature dictionary as in Xue et al [2017]. In a nutshell, the feature learning process can be treated as a sparse encoding problem.…”