{"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/rank-one-nmf-based-initialization-for-nmf-and","title":"Rank-One NMF-Based Initialization for NMF and Relative Error Bounds under a Geometric Assumption","arxiv_id":"1612.08549","date":"2016-12-27","proceeding":null,"authors":["Zhaoqiang Liu","Vincent Y. F. Tan"],"abstract":"We propose a geometric assumption on nonnegative data matrices such that\nunder this assumption, we are able to provide upper bounds (both deterministic\nand probabilistic) on the relative error of nonnegative matrix factorization\n(NMF). The algorithm we propose first uses the geometric assumption to obtain\nan exact clustering of the columns of the data matrix; subsequently, it employs\nseveral rank-one NMFs to obtain the final decomposition. When applied to data\nmatrices generated from our statistical model, we observe that our proposed\nalgorithm produces factor matrices with comparable relative errors vis-\\`a-vis\nclassical NMF algorithms but with much faster speeds. On face image and\nhyperspectral imaging datasets, we demonstrate that our algorithm provides an\nexcellent initialization for applying other NMF algorithms at a low\ncomputational cost. Finally, we show on face and text datasets that the\ncombinations of our algorithm and several classical NMF algorithms outperform\nother algorithms in terms of clustering performance.","url_abs":"http://arxiv.org/abs/1612.08549v2","url_pdf":"http://arxiv.org/pdf/1612.08549v2.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":"rank-one-nmf-based-initialization-for-nmf-and","repo_url":"https://github.com/zhaoqiangliu/cr1-nmf","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}