Kernel two-dimensional ridge regression for subspace clustering

Abstract Subspace clustering methods have been extensively studied in recent years. For 2-dimensional (2D) data, existing subspace clustering methods usually convert 2D examples to vectors, which severely damages inherent structural information and relationships of the original data. In this paper, we propose a novel subspace clustering method, named KTRR, for 2D data. The KTRR provides us with a way to learn the most representative 2D features from 2D data in learning data representation. In particular, the KTRR performs 2D feature learning and low-dimensional representation construction simultaneously, which renders the two tasks to mutually enhance each other. 2D kernel is introduced to the KTRR, which renders the KTRR to have enhanced capability of capturing nonlinear relationships from data. An efficient algorithm is developed for its optimization with provable decreasing and convergent property in objective value. Extensive experimental results confirm the effectiveness and efficiency of our method.