{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/orthogonal-nonnegative-matrix-factorization","title":"Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence","arxiv_id":"2410.07786","date":"2024-10-10","proceeding":null,"authors":["Jean Pacifique Nkurunziza","Fulgence Nahayo","Nicolas Gillis"],"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.","url_abs":"https://arxiv.org/abs/2410.07786v2","url_pdf":"https://arxiv.org/pdf/2410.07786v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"orthogonal-nonnegative-matrix-factorization","repo_url":"https://gitlab.com/ngillis/kl-onmf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"document-classification","task_name":"Document Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}