Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence
Abstract
Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model and algorithm for ONMF that minimizes the Kullback-Leibler (KL) divergence. As opposed to the Frobenius norm which assumes Gaussian noise, the KL divergence is the maximum likelihood estimator for Poisson-distributed data, which can model better sparse vectors of word counts in document data sets and photo counting processes in imaging. We develop an algorithm based on alternating optimization, KL-ONMF, and show that it performs favorably with the Frobenius-norm based ONMF for document classification and hyperspectral image unmixing.
Cite
@article{arxiv.2410.07786,
title = {Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence},
author = {Jean Pacifique Nkurunziza and Fulgence Nahayo and Nicolas Gillis},
journal= {arXiv preprint arXiv:2410.07786},
year = {2025}
}
Comments
10 pages, corrected some typos