Another Robust NMF: Rethinking the Hyperbolic Tangent Function and Locality Constraint

Abstract

Non-negative matrix factorization (NMF) is a classical data analysis tool for clustering tasks. It usually considers the squared loss to measure the reconstruction error, thus it is sensitive to the presence of outliers. Looking into the literature, most of the existing robust NMF models focus on statistics-based robust estimators with known distribution assumptions. Besides those estimators, whether can we seek another function without the distribution assumption to boost the robustness of NMF? To solve the problem, we propose a robust NMF termed as tanhNMF for short, which rethinks the hyperbolic tangent (tanh) function as a robust loss to evaluate the reconstruction error. Moreover, to capture geometric structure within the data, we devise a locality constraint to regularize tanhNMF to model data locality. Owing to the non-convex tanh function, it is non-trivial to optimize tanhNMF. Following the paradigm of the half-quadratic algorithm, we easily solve an adaptive weighted NMF instead of original tanhNMF. The experiments of face clustering on four popular facial datasets with/without corruptions show that the proposed method achieves the satisfactory performance against several representative baselines including NMF and its robust counterparts. This also implies that the proposed tanh function could serve as an alternative robust loss for NMF.