O-Minus Decomposition for Multiview Tensor Subspace Clustering

Yingcong Lu, Yipeng Liu, Zhen Long, Zhangxin Chen, Ce Zhu

Abstract: With the powerful ability to exploit the latent structure of self-representation information, multiple off-the-shelf low rank tensor constraints have been employed in multiview tensor subspace clustering (MTSC) for achieving significant performance. However, current approaches mainly suffer from a series of problems, such as the deficient exploration of self-representation due to the unbalanced unfolding matrices, the inability to simultaneously capture both intraview and interview information, and so forth. All these will lead to MTSC with insufficient access to global information, which is contrary to the target of multiview clustering. To alleviate these problems, we propose a new tensor decomposition called O-minus decomposition (OMD) for multiview clustering. Specifically, based on the tensor ring format, we present the O-minus structure, which consists of a circle with an efficient bridge linking two weakly correlated factors. In this way, the information from intraview and interview can be better obtained simultaneously. Moreover, the enhanced capacity to capture global low-rank information will be achieved. The alternating direction method of multipliers is used to solve the proposed optimization model for OMD-MVC. Numerical experiments on six benchmark datasets demonstrate the superiority of our proposed method in terms of F-score, precision, recall, normalized mutual information, adjusted rand index, and accuracy.