Coupled block diagonal regularization for multi-view subspace clustering

The object of multi-view subspace clustering is to uncover the latent low-dimensional structure by segmenting a collection of high-dimensional multi-source data into their corresponding subspaces. Existing methods imposed various constraints on the affinity matrix and/or the cluster labels to promote segmentation accuracy, and demonstrated effectiveness in some applications. However, the previous constraints are inefficient to ensure the ideal discriminative capability of the corresponding method. In this paper, we propose to learn view-specific affinity matrices and a common cluster indicator matrix jointly in a unified minimization problem, in which the affinity matrices and the cluster indicator matrix can guide each other to facilitate the final segmentation. To enforce the ideal discrimination, we use a block diagonal inducing regularity to constrain the affinity matrices as well as the cluster indicator matrix. Such coupled regularities are double insurances to promote clustering accuracy. We call it Coupled Block Diagonal Regularized Multi-view Subspace Clustering (CBDMSC). Based on the alternative minimization method, an algorithm is proposed to solve the new model. We evaluate our method by several metrics and compare it with several state-of-the-art related methods on some commonly used datasets. The results demonstrate that our method outperforms the state-of-the-art methods in the vast majority of metrics.