Locality-constrained least squares regression for subspace clustering

Low-rank representation (LRR) is a typical data representation method that has been developed in recent years. Based on the main idea of LRR, least squares regression (LSR) constructs a new optimization problem to group the highly correlated data together. Compared with other LRR algorithms that are sophisticated, LSR is simpler and more efficient. It is a linear representation method that captures the global structure of data with a low-rank constraint. Research has shown that locality constraints typically improve the discrimination of the representation and demonstrate better performance than those "non-local" methods for image recognition tasks. To combine LSR and the locality constraints, we propose a novel data representation method called locality-constrained LSR (LCLSR) for subspace clustering. LCLSR forces the representation to prefer the selection of neighborhood points. The locality constraint is calculated based on the Euclidean distances between data points. Under the locality constraint, the obtained affinity matrix captures the locally linear relationship for data points lie on a nonlinear manifold. We propose three approaches to obtain the locality constraint and compare their performance with other related work on subspace clustering. We conducted extensive experiments on several datasets for subspace clustering. The results demonstrated that the proposed DCLSR, LCLSR epsilon, and LCLSRk substantially outperformed state-of-the-art subspace clustering methods. (C) 2018 Elsevier B.V. All rights reserved.