Robust distribution-based nonnegative matrix factorizations for dimensionality reduction

As a popular dimensionality-reduction technique, nonnegative matrix factorization (NMF) has been widely researched since it is consistent with human cognitive processes in the psychology and physiology. This paper presents a novel NMF framework, called robust distribution-based NMF (RDNMF), to learn the robustly discriminative representations for data. In this RDNMF, a Kullback-Leibler divergence to measure the similarity between the data and representations is introduced, which fully preserves the geometrical structure of data. Meanwhile, this RDNMF employs the l(2),(1)-norm loss to reduce the influence of noise and outliers. This paper further proposes a semi-supervised RDNMF (SRDNMF) by enforcing the representations of labeled points in the same class to be aligned on the same axis. The proposed RDNMF and SRDNMF are solved by the modified multiplicative update rules. Clustering experiments on seven benchmark datasets demonstrate the effectiveness of our methods in comparison to other state-of-the-art methods. (C) 2020 Elsevier Inc. All rights reserved.