{"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/compact-factorization-of-matrices-using","title":"Compact Factorization of Matrices Using Generalized Round-Rank","arxiv_id":"1805.00184","date":"2018-05-01","proceeding":null,"authors":["Pouya Pezeshkpour","Carlos Guestrin","Sameer Singh"],"abstract":"Matrix factorization is a well-studied task in machine learning for compactly\nrepresenting large, noisy data. In our approach, instead of using the\ntraditional concept of matrix rank, we define a new notion of link-rank based\non a non-linear link function used within factorization. In particular, by\napplying the round function on a factorization to obtain ordinal-valued\nmatrices, we introduce generalized round-rank (GRR). We show that not only are\nthere many full-rank matrices that are low GRR, but further, that these\nmatrices cannot be approximated well by low-rank linear factorization. We\nprovide uniqueness conditions of this formulation and provide gradient\ndescent-based algorithms. Finally, we present experiments on real-world\ndatasets to demonstrate that the GRR-based factorization is significantly more\naccurate than linear factorization, while converging faster and using lower\nrank representations.","url_abs":"http://arxiv.org/abs/1805.00184v1","url_pdf":"http://arxiv.org/pdf/1805.00184v1.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":"compact-factorization-of-matrices-using","repo_url":"https://github.com/pouyapez/GRR-Matrix-Factorization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}