Robust Adaptive Graph Regularized Non-Negative Matrix Factorization

Abstract

Data clustering, which aims to divide the given samples into several different groups, has drawn much attention in recent years. As a powerful tool, non-negative matrix factorization (NMF) has been applied successfully in clustering tasks. However, there are still two main limitations. First, the original NMF treats equally both noisy and clean data, which leads to high sensitivity to noises and outliers. Second, the performance of graph-based NMFs highly depends on the input graph, that is, if a low-quality graph is constructed to regularize NMF, the clustering results will be bad. To address the above-mentioned problems, we propose a novel robust adaptive graph regularized non-negative matrix factorization (RAGNMF) for data clustering. To be specific, we develop a robust weighted NMF (RWNMF) that can assign small weights to noises and outliers and large weights to clean data. Thus, the robustness of NMF is improved. Moreover, in the process of matrix factorization, metric learning is combined to choose some discriminative features and compute more appropriate distances of samples. Then, an adaptive graph is learned to well regularize the NMF. The experimental results demonstrate that the proposed RAGNMF can achieve better clustering performance then most of the state-of-the-art methods.