Enhanced Nonconvex Low-Rank Approximation of Tensor Multi-Modes for Tensor Completion

Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by approximation theory, researchers have proposed a series of effective completion methods. However, most these methods directly consider the global low-rankness underlying tensors, which is not sufficient for low sampling rate; addition, single nuclear norm or its relaxation usually adopted to approximate rank function, would lead suboptimal solution deviated from original one. To alleviate above problems, this paper, we propose novel multi-modes (LRATM), double nonconvex L ? designed represent joint-manifold drawn factorization factors each mode tensor. A block successive upper-bound minimization method-based algorithm efficiently solve model, it can be demonstrated that our numerical scheme converges coordinate-wise minimizers. Numerical results on three types public multi-dimensional datasets tested shown recover variety tensors with significantly fewer samples than compared