Zhou Pan, Lu Canyi, Feng Jiashi, Lin Zhouchen, Yan Shuicheng
IEEE Trans Pattern Anal Mach Intell. 2021 May;43(5):1718-1732. doi: 10.1109/TPAMI.2019.2954874. Epub 2021 Apr 1.
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.
多向或张量数据分析近来已引起越来越多的关注，在实际中有许多重要应用。本文提出了一种张量低秩表示（TLRR）方法，这是第一种能够精确恢复具有内在低秩结构的干净数据并对其进行准确聚类的方法，且具有可证明的性能保证。特别地，对于具有任意稀疏损坏的张量数据，TLRR在温和条件下能够精确恢复干净数据；同时，TLRR能够精确验证其真实的原始张量子空间，从而对它们进行准确聚类。TLRR目标函数可通过具有收敛保证的高效凸规划进行优化。此外，我们提供了两种简单而有效的字典构造方法，即简单TLRR（S-TLRR）和鲁棒TLRR（R-TLRR），分别用于处理轻度和严重损坏的数据。在图像/视频恢复和人脸聚类这两个计算机视觉数据分析任务上的实验结果，清楚地证明了我们所提出的方法相对于包括流行的LRR和SSC方法在内的现有技术具有卓越的性能、效率和鲁棒性。
