CIS Publication Spotlight [Publication Spotlight]
Digital Object Identifier: 10.1109/ TNNLS.2012.2235082 nonconvex framework is proposed for learning the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, this method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. It includes how to combine the widely used Lp norm (0<p<1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a major ization–minimization (MM)type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls in to the genera l f r amework of reweighed approaches. It is proved that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust pr incipa l component analysis and low-rank representation. Exper imental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0<p<1) for both data with higher rank and with denser corruptions.”