Automatic Relevance Determination in Nonnegative Matrix Factorization Based on a Zero-Inflated Compound Poisson-Gamma Distribution

Abstract

In this paper, we consider the determination of the number of factors in nonnegative matrix factorization (NMF) for a zero-inflated data matrix. This zero-inflated case leads to poor approximation to the nonnegative data matrix. To address this problem, we use the zero-inflated compound Poisson-gamma distribution as the error distribution in NMF. In addition, we consider automatic relevance determination (ARD) for model order selection. Our simulation study shows that our method is better than the basic ARD method for zero-inflated data. We apply our proposed method to real-world purchasing data to determine the number of buying patterns.