Low Rank Regularization: A review

Low Rank Regularization (LRR), in essence, involves introducing a low rank or approximately assumption to target we aim learn, which has achieved great success many data analysis tasks. Over the last decade, much progress been made theories and applications. Nevertheless, intersection between these two lines is rare. In order construct bridge practical applications theoretical studies, this paper provide comprehensive survey for LRR. Specifically, first review recent advances issues that all LRR models are faced with: (1) rank-norm relaxation, seeks find relaxation replace minimization problem; (2) model optimization, use an efficient optimization algorithm solve relaxed models. For issue, detailed summarization various functions conclude non-convex relaxations can alleviate punishment bias problem compared with convex relaxations. second summarize representative algorithms used previous analyze their advantages disadvantages. As main goal of promote application relaxations, conduct extensive experiments compare different functions. The experimental results demonstrate generally large advantage over Such result inspiring further improving performance existing