{"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/primal-dual-algorithms-for-non-negative","title":"Primal-Dual Algorithms for Non-negative Matrix Factorization with the Kullback-Leibler Divergence","arxiv_id":"1412.1788","date":"2014-12-04","proceeding":null,"authors":["Felipe Yanez","Francis Bach"],"abstract":"Non-negative matrix factorization (NMF) approximates a given matrix as a\nproduct of two non-negative matrices. Multiplicative algorithms deliver\nreliable results, but they show slow convergence for high-dimensional data and\nmay be stuck away from local minima. Gradient descent methods have better\nbehavior, but only apply to smooth losses such as the least-squares loss. In\nthis article, we propose a first-order primal-dual algorithm for non-negative\ndecomposition problems (where one factor is fixed) with the KL divergence,\nbased on the Chambolle-Pock algorithm. All required computations may be\nobtained in closed form and we provide an efficient heuristic way to select\nstep-sizes. By using alternating optimization, our algorithm readily extends to\nNMF and, on synthetic examples, face recognition or music source separation\ndatasets, it is either faster than existing algorithms, or leads to improved\nlocal optima, or both.","url_abs":"http://arxiv.org/abs/1412.1788v1","url_pdf":"http://arxiv.org/pdf/1412.1788v1.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":"primal-dual-algorithms-for-non-negative","repo_url":"https://github.com/felipeyanez/nmf","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"primal-dual-algorithms-for-non-negative","repo_url":"https://github.com/fnyanez/nmf","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"face-recognition","task_name":"Face Recognition"},{"task_slug":"music-source-separation","task_name":"Music Source Separation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}