{"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/factoring-nonnegative-matrices-with-linear","title":"Factoring nonnegative matrices with linear programs","arxiv_id":"1206.1270","date":"2012-06-06","proceeding":"NeurIPS 2012 12","authors":["Victor Bittorf","Benjamin Recht","Christopher Re","Joel A. Tropp"],"abstract":"This paper describes a new approach, based on linear programming, for\ncomputing nonnegative matrix factorizations (NMFs). The key idea is a\ndata-driven model for the factorization where the most salient features in the\ndata are used to express the remaining features. More precisely, given a data\nmatrix X, the algorithm identifies a matrix C such that X approximately equals\nCX and some linear constraints. The constraints are chosen to ensure that the\nmatrix C selects features; these features can then be used to find a low-rank\nNMF of X. A theoretical analysis demonstrates that this approach has guarantees\nsimilar to those of the recent NMF algorithm of Arora et al. (2012). In\ncontrast with this earlier work, the proposed method extends to more general\nnoise models and leads to efficient, scalable algorithms. Experiments with\nsynthetic and real datasets provide evidence that the new approach is also\nsuperior in practice. An optimized C++ implementation can factor a\nmultigigabyte matrix in a matter of minutes.","url_abs":"http://arxiv.org/abs/1206.1270v2","url_pdf":"http://arxiv.org/pdf/1206.1270v2.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":"factoring-nonnegative-matrices-with-linear","repo_url":"https://github.com/martinResearch/PySparseLP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1206.1270","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}