arXiv Machine Learning October 19, 2026 By Eric Weine, Peter Carbonetto, Rafael A. Irizarry, Matthew Stephens

A New Family of Poisson Non-negative Matrix Factorization Methods Using the Shifted Log Link

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The paper introduces a new family of Poisson non‑negative matrix factorization (NMF) methods that use a shifted‑log link function, allowing the model to transition from additive to more multiplicative part combinations via a single tuning parameter. An algorithm for maximum‑likelihood fitting and a computationally efficient approximation for large, sparse datasets are presented. Experiments on various real datasets demonstrate that the choice of link function can significantly affect results and may enhance interpretability compared to standard additive Poisson NMF.

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