Robust Nonconvex Nonnegative Low-rank Representation

Low-rank representation (LRR) has drawn increasing attention in many areas due to its pleasing efficiency in finding subspaces in high-dimensional data. However, the performance of LRR is effected by two problems. First, LRR may generate negative coding coefficients which lack physical meaning. Second, LRR usually obtains a suboptimal solution since the nuclear norm ||. ||* is a loose approximation of the rank function rank(.). To solve the limitations simultaneously, we propose a novel model named Robust Nonconvex Nonnegative Low-rank Representation, termed as RNNLRR. Besides, to rule out the trivial solution, diagonal elements of the coding coefficients are constrained to zero. Based on the alternating direction method of multipliers, an efficient optimization algorithm is derived to solve our model. Experiments on data clustering and noise removal demonstrate the superiority of the proposed RNNLRR.