Symmetric Nonnegative Matrix Factorization Based on Box-Constrained Half-Quadratic Optimization

Abstract

Nonnegative Matrix Factorization (NMF) based on half-quadratic (HQ) functions was proven effective and robust when dealing with data contaminated by continuous occlusion according to the half-quadratic optimization theory. Nonetheless, state-of-the-art HQ NMF still cannot handle symmetric data matrices, and this caused problems when applications require processing symmetric matrices, e.g., similarity matrices. In view of such, this study presents HQ Symmetric NMF along with HQ optimization algorithms that can solve symmetric matrix decomposition and avoid oscillations during alternating updates. Moreover, variants of HQ Symmetric NMF are proposed and examined in this study - The direct method and the asymmetry penalty constrained method. Both show their distinct advantages. Experiments on open datasets were conducted for comparison with other methods. Experimental results showed that the proposed HQ Symmetric NMF was more robust against continuous occlusion than the baselines. Both root-mean-squared errors and coefficients of determination were better than those of the baselines, thereby demonstrating effectiveness of the proposed method.

Keywords

• Half-quadratic optimization
• symmetric nonnegative matrix factorization
• similarity matrix