Enforced block diagonal subspace clustering with closed form solution

Abstract

Subspace clustering aims to fit each category of data points by learning an underlying subspace and then conduct clustering according to the learned subspace. Ideally, the learned subspace is expected to be block diagonal such that the similarities between clusters are zeros. In this paper, we provide the explicit theoretical connection between spectral clustering and the subspace clustering based on block diagonal representation. We propose Enforced Block Diagonal Subspace Clustering (EBDSC) and show that the spectral clustering with the Radial Basis Function kernel can be regarded as EBDSC. Compared with the exiting subspace clustering methods, an analytical, nonnegative and symmetrical solution can be obtained by EBDSC. An important difference with respect to the existing ones is that our model is a more general case. EBDSC directly uses the obtained solution as the similarity matrix, which can avoid the complex computation of the optimization program. Then the solution obtained by the proposed method can be used for the final clustering. Finally, we provide the experimental analysis to show the efficiency and effectiveness of our method on the synthetic data and several benchmark data sets in terms of different metrics.