Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence
<|reference_start|>Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence: 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 vectors of word counts in document data sets and photo counting processes in imaging. We have developed 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.<|reference_end|>
@article{nkurunziza2024orthogonal,
    title={Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler
  divergence},
    author={Jean Pacifique Nkurunziza, Fulgence Nahayo, Nicolas Gillis},
    journal={arXiv preprint arXiv:2410.07786},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.07786},
    primaryClass={stat.ML cs.IR cs.LG eess.SP}
}