Generalized Poisson Matrix Factorization for Overdispersed Count Data

TL;DR

This paper introduces a generalized Poisson matrix factorization model that effectively handles overdispersed count data, overcoming limitations of previous Poisson and negative binomial models.

Contribution

It proposes a novel NMF framework based on the generalized Poisson distribution, enhancing flexibility and applicability for overdispersed count data.

Findings

The model accurately captures overdispersion in count data.

It outperforms traditional Poisson and negative binomial models.

The approach is validated on real-world datasets.

Abstract

Non-negative matrix factorization (NMF) is widely used as a feature extraction technique for matrices with non-negative entries, such as image data, purchase histories, and other types of count data. In NMF, a non-negative matrix is decomposed into the product of two non-negative matrices, and the approximation accuracy is evaluated by a loss function. If the Kullback-Leibler divergence is chosen as the loss function, the estimation coincides with maximum likelihood under the assumption that the data entries are distributed according to a Poisson distribution. To address overdispersion, negative binomial matrix factorization has recently been proposed as an extension of the Poisson-based model. However, the negative binomial distribution often generates an excessive number of zeros, which limits its expressive capacity. In this study, we propose a non-negative matrix factorization based on the generalized Poisson distribution, which can flexibly accommodate overdispersion, and we introduce a maximum likelihood approach for parameter estimation. This methodology provides a more versatile framework than existing models, thereby extending the applicability of NMF to a broader class of count data.