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arXiv · 2410.07786

Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence

Jean Pacifique Nkurunziza·Fulgence Nahayo·Nicolas Gillis
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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.

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BibTeXRIS

Jean Pacifique Nkurunziza, Fulgence Nahayo, Nicolas Gillis. 2024-10-10. Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence. https://doi.org/10.1016/j.patrec.2025.08.012

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