Tensor Low-Rank Representation for Data Recovery and Clustering

Multi-way or tensor data analysis has attracted increasing attention recently, with many important applications in practice. This article develops a tensor low-rank representation (TLRR) method, which is the first approach that can exactly recover the clean data of intrinsic low-rank structure and accurately cluster them as well, with provable performance guarantees. In particular, for tensor data with arbitrary sparse corruptions, TLRR can exactly recover the clean data under mild conditions; meanwhile TLRR can exactly verify their true origin tensor subspaces and hence cluster them accurately. TLRR objective function can be optimized via efficient convex programing with convergence guarantees. Besides, we provide two simple yet effective dictionary construction methods, the simple TLRR (S-TLRR) and robust TLRR (R-TLRR), to handle slightly and severely corrupted data respectively. Experimental results on two computer vision data analysis tasks, image/video recovery and face clustering, clearly demonstrate the superior performance, efficiency and robustness of our developed method over state-of-the-arts including the popular LRR and SSC methods.