Robust Bi-stochastic Graph Regularized Matrix Factorization for Data Clustering
Qi Wang, Xiang He, Jiang Xu, Xuelong Li
Abstract
Data clustering, which is to partition the given data into different groups, has attracted much attention. Recently various effective algorithms have been developed to tackle the task. Among these methods, non-negative matrix factorization (NMF) has been demonstrated to be a powerful tool. However, there are still some problems. First, the standard NMF is sensitive to noises and outliers. Although <inline-formula><tex-math notation="LaTeX">$\ell _{2,1}$</tex-math></inline-formula> norm based NMF improves the robustness, it is still affected easily by large noises. Second, for most graph regularized NMF, the performance highly depends on the initial similarity graph. Third, many graph-based NMF models perform the graph construction and matrix factorization in two separated steps. Thus the learned graph structure may not be optimal. To overcome the above drawbacks, we propose a robust bi-stochastic graph regularized matrix factorization (RBSMF) framework for data clustering. Specifically, we present a general loss function, which is more robust than the commonly used <inline-formula><tex-math notation="LaTeX">$L_2$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$L_1$</tex-math></inline-formula> functions. Besides, instead of keeping the graph fixed, we learn an adaptive similarity graph. Furthermore, the graph updating and matrix factorization are processed simultaneously, which can make the learned graph more appropriate for clustering. Extensive experiments have shown the proposed RBSMF outperforms other state-of-the-art methods.