A Robust Sparse Nonnegative Matrix Factorization with Low Rank representation for clustering

Abstract

Nonnegative Factorization Matrix has achieved excellent results in the field of data mining and machine learning. However, NMF and its extensions, use the least square error function, are sensitive to noises and simultaneously ignore some useful discriminant information in the error matrix. To tackle this issue, we propose a novel method, named Robust Sparse Nonnegative Matrix Factorization with Low Rank (RSLR-NMF), in this paper. RSLR-NMF can effectively remove any redundant information from the input data and extract the hidden information in the noisy error part based on Bilinear Error Matrix Decomposition (BEMD) module. RSLR-NMF takes into account reconstruction error matrix and low rank error matrix simultaneously with norm constraint and low rank constraint, respectively. Besides, elegant updating rules are presented to solve the proposed method. The experimental results on several data sets show that the proposed RSLR-NMF provides more faithful basis factors and effective clustering results.