Non-negative matrix factorization via adaptive sparse graph regularization

Abstract

Non-negative matrix factorization (NMF), as an efficient and intuitive dimension reduction algorithm, has been successfully applied to clustering tasks. However, there are still two dominating limitations. First, the original NMF only pays attention to the global data structure, ignoring the intrinsic geometry of the original higher-dimensional data. Second, the traditional pairwise distance-based graph construction is sensitive to noise and outliers, and the nearest neighbor graph obtained is not optimal. As a result, the clustering performance will be reduced. To solve the aforementioned problems and increase the cluster accuracy, a non-negative matrix factorization via adaptive sparse graph (NMF_ASGR) is proposed in this paper. More precisely, this paper assembles the sparse representation and manifold learning into a framework to get the l1 sparse robust graph. The l1 sparse robust graph not only can adaptively discover the potential manifold structure of the data, but also has strong robustness to noise and outliers, which makes the structure of the graph can be learned automatically in the process of matrix decomposition. Moreover, an adaptive sparse graph is learned to batter regularize the NMF. Finally, the effectiveness and superiority of the proposed algorithm are illustrated by lots of image clustering experiments.