A Folded Concave Penalty Regularized Subspace Clustering Method to Integrate Affinity and Clustering

Abstract

Most sparse or low-rank-based subspace clustering methods divide the processes of getting the affinity matrix and the final clustering result into two independent steps. We propose to integrate the affinity matrix and the data labels into a minimization model. Thus, they can interact and promote each other and finally improve clustering performance. Furthermore, the block diagonal structure of the representation matrix is most preferred for subspace clustering. We define a folded concave penalty (FCP) based norm to approximate rank function and apply it to the combination of label matrix and representation vector. This FCP-based regularization term can enforce the block diagonal structure of the representation matrix effectively. We minimize the difference of l1 norm and l2 norm of the label vector to make it have only one nonzero element since one data only belong to one subspace. The index of that nonzero element is associated with the subspace from which the data come and can be determined by a variant of graph Laplacian regularization. We conduct experiments on several popular datasets. The results show our method has better clustering results than several state-of-the-art methods.