Kernel Subspace Clustering based on Block Diagonal Representation and Sparse Constraints

Abstract

Subspace clustering is an effective method for high-dimensional data clustering. On the premise of global linearity of data, it uses data self-representation to reconstruct each sample linearly, and achieves good results. However, the actual original data structure is usually nonlinear, which makes the subspace clustering algorithm designed on the premise of linear subspace not achieve satisfactory results in dealing with nonlinear data. In order to deal with nonlinear data better, we use kernel function to introduce block diagonal structure and sparse prior into kernel feature space, and propose a kernel subspace clustering method based on block diagonal representation and sparse constraints (KSCBS). Firstly, we perform subspace learning by combining block diagonal representation and sparse constraints. In this way, the obtained coefficient matrix can maintain the block diagonal structure and better reveal the real attributes of the data. Secondly, we use the kernel technique to map the nonlinear original data space into the appropriate high-dimensional feature space, and then transform it into linear data for processing to solve the nonlinear problem of subspace data. Finally, we use the alternating minimization algorithm to solve the objective function. Compared with other advanced linear subspace and nonlinear subspace algorithms, our algorithm has better clustering performance on several common data sets.