Low-Rank Regularized Heterogeneous Tensor Decomposition for Subspace Clustering

Abstract

This letter proposes a low-rank regularized heterogeneous tensor decomposition (LRRHTD) algorithm for subspace clustering, in which various constrains in different modes are incorporated to enhance the robustness of the proposed model. Specifically, due to the presence of noise and redundancy in the original tensor, LRRHTD seeks a set of orthogonal factor matrices for all but the last mode to map the high-dimensional tensor into a low-dimensional latent subspace. Furthermore, by imposing a low-rank constraint on the last mode, which is relaxed by using a nuclear norm, the lowest rank representation that reveals the global structure of samples is obtained for the purpose of clustering. We develop an effective algorithm based on the augmented Lagrange multiplier to optimize our model. Experiments on two public datasets demonstrate that our method reaches convergence within a small number of iterations and achieves promising results in comparison with the state of the arts.