Robust subspace clustering via symmetry constrained latent low rank representation with converted nuclear norm

Abstract

Subspace clustering, which is devoted to classifying data samples derived from a union of linear subspaces, has been widely applied to various fields such as pattern recognition, artificial intelligence and computer vision. In this paper, we propose a symmetry constrained latent low rank representation with converted nuclear norm (SLLRRC) algorithm for robust subspace clustering, which extends the original latent low rank representation (LLRR) algorithm by introducing a kind of converted nuclear norm and integrating strategy of the symmetric constraint. SLLRRC both enhances the sparsity of the coefficient matrix and guarantees weight consistency for each pair of data samples when seeking the low rank representation. The symmetric coefficient matrix that will no longer be overly dense is acquired by the inexact augmented Lagrange multipliers (IALM) method. With further exploiting the angular information of the principal directions of that, the sparse affinity matrix for spectral clustering is identified. Extensive experimental results on face clustering and motion segmentation datasets confirm the availability and robustness of the proposed algorithm, and it is highly competitive compared to the state-of-the-art subspace clustering algorithms.