{"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/convex-factorization-machine-for-regression","title":"Convex Factorization Machine for Regression","arxiv_id":"1507.01073","date":"2015-07-04","proceeding":null,"authors":["Makoto Yamada","Wenzhao Lian","Amit Goyal","Jianhui Chen","Kishan Wimalawarne","Suleiman A. Khan","Samuel Kaski","Hiroshi Mamitsuka","Yi Chang"],"abstract":"We propose the convex factorization machine (CFM), which is a convex variant\nof the widely used Factorization Machines (FMs). Specifically, we employ a\nlinear+quadratic model and regularize the linear term with the\n$\\ell_2$-regularizer and the quadratic term with the trace norm regularizer.\nThen, we formulate the CFM optimization as a semidefinite programming problem\nand propose an efficient optimization procedure with Hazan's algorithm. A key\nadvantage of CFM over existing FMs is that it can find a globally optimal\nsolution, while FMs may get a poor locally optimal solution since the objective\nfunction of FMs is non-convex. In addition, the proposed algorithm is simple\nyet effective and can be implemented easily. Finally, CFM is a general\nfactorization method and can also be used for other factorization problems\nincluding including multi-view matrix factorization and tensor completion\nproblems. Through synthetic and movielens datasets, we first show that the\nproposed CFM achieves results competitive to FMs. Furthermore, in a\ntoxicogenomics prediction task, we show that CFM outperforms a state-of-the-art\ntensor factorization method.","url_abs":"http://arxiv.org/abs/1507.01073v5","url_pdf":"http://arxiv.org/pdf/1507.01073v5.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":"convex-factorization-machine-for-regression","repo_url":"https://github.com/karunru/ConvexFactorizationMachines.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}