Abstract: Focus on the problems that the linear block diagonal representation subspace clustering cannot effectively handle non-linear visual data, and the regular regularizers cannot directly pursue the k-block diagonal matrix, a kernel block diagonal representation subspace clustering is proposed. In the proposed algorithm, the original input space is mapped into the kernel Hilbert space which is linearly separable, and the spectral clustering is performed in the feature space. The convergence analysis is given, and the strong convex of variables and the boundedness of function is utilized to verify the monotonically decreasing of objective function and the boundedness and convergence of the affinity matrix, which breaks through the difficulty of convergence proof. Compared with other algorithms such as the kernel sparse subspace clustering and the block diagonal representation algorithm tested, the algorithm has achieved the lower clustering error and higher normalized mutual information on Extended Yale B, ORL and MVtec ITODD.

Key words: visual data, kernel subspace clustering, block diagonal representation, convergence analysis