Graph Regularized Sparse L2,1 Semi‐Nonnegative Matrix Factorization for Data Reduction

Abstract

ABSTRACTNon‐negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi‐Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts‐based data representations to include mixed‐sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF‐related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new SNF algorithm that utilizes the noise‐insensitive norm. We provide monotonic convergence analysis of the SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed‐sign datasets as well as several randomized mixed‐sign matrices to demonstrate the performance superiority of SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels.