Kernel Block Diagonal Representation Subspace Clustering with Similarity Preservation

Subspace clustering methods based on the low-rank and sparse model are effective strategies for high-dimensional data clustering. However, most existing low-rank and sparse methods with self-expression can only deal with linear structure data effectively, but they cannot handle data with complex nonlinear structure well. Although kernel subspace clustering methods can efficiently deal with nonlinear structure data, some similarity information between samples may be lost when the original data are reconstructed in the kernel space. Moreover, these kernel subspace clustering methods may not obtain an affinity matrix with an optimal block diagonal structure. In this paper, we propose a novel subspace clustering method termed kernel block diagonal representation subspace clustering with similarity preservation (KBDSP). KBDSP contains three contributions: (1) an affinity matrix with block diagonal structure is generated by introducing a block diagonal representation term; (2) a similarity-preserving regularizer is constructed and embedded into our model by minimizing the discrepancy between inner products of original data and inner products of reconstructed data in the kernel space, which better preserve the similarity information between original data; (3) the KBDSP model is proposed by integrating the block diagonal representation term and similarity-preserving regularizer into the kernel self-expressing frame. The optimization of our proposed model is solved efficiently by utilizing the alternating direction method of multipliers (ADMM). Experimental results on nine datasets demonstrate the effectiveness of the proposed method.