{"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/provable-alternating-gradient-descent-for-non","title":"Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlations","arxiv_id":"1706.04097","date":"2017-06-13","proceeding":"ICML 2017 8","authors":["Yuanzhi Li","YIngyu Liang"],"abstract":"Non-negative matrix factorization is a basic tool for decomposing data into\nthe feature and weight matrices under non-negativity constraints, and in\npractice is often solved in the alternating minimization framework. However, it\nis unclear whether such algorithms can recover the ground-truth feature matrix\nwhen the weights for different features are highly correlated, which is common\nin applications. This paper proposes a simple and natural alternating gradient\ndescent based algorithm, and shows that with a mild initialization it provably\nrecovers the ground-truth in the presence of strong correlations. In most\ninteresting cases, the correlation can be in the same order as the highest\npossible. Our analysis also reveals its several favorable features including\nrobustness to noise. We complement our theoretical results with empirical\nstudies on semi-synthetic datasets, demonstrating its advantage over several\npopular methods in recovering the ground-truth.","url_abs":"http://arxiv.org/abs/1706.04097v1","url_pdf":"http://arxiv.org/pdf/1706.04097v1.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":"provable-alternating-gradient-descent-for-non","repo_url":"https://github.com/PrincetonML/AND4NMF","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.04097","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}