Selecting β-Divergence for Nonnegative Matrix Factorization by Score Matching

Nonnegative Matrix Factorization (NMF) based on the family of β-divergences has shown to be advantageous in several signal processing and data analysis tasks. However, how to automatically select the best divergence among the family for given data remains unknown. Here we propose a new estimation criterion to resolve the problem of selecting β. Our method inserts the point estimate of factorizing matrices from β-NMF into a Tweedie distribution that underlies β-divergence. Next, we adopt a recent estimation method called Score Matching for β selection in order to overcome the difficulty of calculating the normalizing constant in Tweedie distribution. Our method is tested on both synthetic and real-world data. Experimental results indicate that our selection criterion can accurately estimate β compared to ground truth or established research findings.