Sparse subspace clustering algorithm with non-convex constraints

Abstract

Key of sparse subspace clustering is to solve an optimization problem based on sparse penalty term to obtain sparse representation coefficients. Ideal sparsity penalty term is ℓ0-norm, but the optimization problem based on the ℓ0-norm is NP-hard. At present, most methods for solving sparse coefficients use the convex relaxation of the ℓ0-norm, ℓ0-norm as a penalty term, but it can not well describe the sparsity of the representation coefficients. Therefore, In this paper, a nonconvex φα energy functional is used to replace the ℓ0-norm in the objective function and a sparse subspace clustering algorithm based on non-convex φα energy functional is proposed, compared with the traditional ℓ1-norm, non-convex φα energy functional increases the sparsity of the representation coefficients and obtains a better similarity matrix, where α ⪆ 0 is a parameter that regulates the degree of non-convex constraints. In addition, the alternating direction method of multipliers is used to solve the optimization problem with non-convex constraints. Experiments on synthetic datasets and face datasets show that the proposed algorithm reduces the error rate of clustering.