Graph Regularized Subspace Clustering via Low-Rank Decomposition

Subspace clustering (SC) is able to identify low-dimensional subspace structures embedded in high-dimensional data. Recently, graph-regularized approaches aim to tackle this problem by learning a linear representation of data samples and also a graph structure in a unified framework. However, previous approaches exploit a graph embedding term based on representation matrix, which could over-smooth the graph structure and thus adversely affect the clustering performance. In this paper, we present a novel algorithm based on joint low-rank decomposition and graph learning from data samples. In graph learning, only a low-rank component of the representation matrix is employed to construct the graph embedding term. An alternating direction method of multipliers (ADMM) is further developed to tackle the resulting nonconvex problem. Experimental results on both synthetic data and real benchmark databases validate the effectiveness of the proposed SC algorithm.