Generalized Poisson Matrix Factorization for Overdispersed Count Data
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914227780845568 |
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| author | Ohashi, Ryo Abe, Hiroyasu Sakaori, Fumitake |
| author_facet | Ohashi, Ryo Abe, Hiroyasu Sakaori, Fumitake |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Poisson Matrix Factorization for Overdispersed Count Data Ohashi, Ryo Abe, Hiroyasu Sakaori, Fumitake Computation Methodology 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. |
| title | Generalized Poisson Matrix Factorization for Overdispersed Count Data |
| topic | Computation Methodology |
| url | https://arxiv.org/abs/2512.24604 |