Adaptive graph regularization method based on least square regression for clustering

Abstract

The low-rank representation with adaptive graph regularization (LRAGR) method has been successfully proposed for clustering applications, since it can solve the problems of missing local information and unclear graph structure in data clustering tasks. However, LRAGR utilizes the low-rank representation technique to mine data information, which makes the obtained coefficient matrix too dense and is not conducive to cluster division. Moreover, due to the singular value decomposition, the constraint of the coefficient matrix requires high computational complexity and is difficult to be applied in practical tasks. To address the above issues, in this paper, a new adaptive graph regularization method, called the adaptive graph regularization method based on least squares regression (LSAGR), is proposed for data clustering applications. Specifically, the proposed LSAGR method adopts the Frobenius norm instead of kernel norm to approximate the rank function to satisfy the clustering effect, that is, the coefficients of the cluster-related data are approximately equal. Compared with the traditional LRAGR method, in clustering tasks, the LSAGR method can better reveal the real subspace membership, improve the clustering performance and reduce the computational complexity. Finally, extensive experimental results demonstrate that, compared with several related state-of-the-art methods, the proposed LSAGR method usually has better clustering performance on six real-world image datasets in clustering applications.