A Unified View of Nonconvex Heuristic Approach for Low-Rank and Sparse Structure Learning

Learning the intrinsic data structures via matrix analysis has received wide attention in many fields, e.g., neural networks [23], machine learning [21] [29], financial engineering [12], computer vision [3] [36] [13] and pattern recognition [11] [31]. There are quite a number of efficient mathematical tools for rank analysis, e.g., Principal Component Analysis (PCA) and Singular Value Decomposition (SVD). However, these typical approaches could only handle some preliminary and simple problems. With the recent progress of compressive sensing [15], a new concept on nuclear norm optimization has emerged into the field of rank minimization [35] and has led to a number of interesting applications, e.g., low-rank structure learning (LRSL) from corruptions and background modeling [10].37