An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence
Nonnegative Matrix Factorization (NMF) is a fundamental tool in unsupervised learning, which approximates a nonnegative matrix by the product of two low-rank nonnegative factors. The Kullback-Leibler (KL) divergence is best suited to measure the data to model discrepancy when the decomposed data sample follows a Poisson distribution, which is the case for count datasets such as term-document matrices or images. Most KL-NMF algorithms in the literature minimize a separable majorant of the loss to find their next iterate. We argue that this method has reached its limits and propose to use instead the second-order Taylor expansion of the loss, leading to a Newton-type method. We minimize thi...
| Authors | Damien Lesens, Jérémy E. Cohen, Bora Uçar |
|---|---|
| Primary category | cs.LG |
| Published | 15 July 2026 |
| Last updated at source | 15 July 2026 |
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