{"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/relative-pairwise-relationship-constrained","title":"Relative Pairwise Relationship Constrained Non-negative Matrix Factorisation","arxiv_id":"1803.02218","date":"2018-03-05","proceeding":null,"authors":["Shuai Jiang","Kan Li","Richard Yida Xu"],"abstract":"Non-negative Matrix Factorisation (NMF) has been extensively used in machine\nlearning and data analytics applications. Most existing variations of NMF only\nconsider how each row/column vector of factorised matrices should be shaped,\nand ignore the relationship among pairwise rows or columns. In many cases, such\npairwise relationship enables better factorisation, for example, image\nclustering and recommender systems. In this paper, we propose an algorithm\nnamed, Relative Pairwise Relationship constrained Non-negative Matrix\nFactorisation (RPR-NMF), which places constraints over relative pairwise\ndistances amongst features by imposing penalties in a triplet form. Two\ndistance measures, squared Euclidean distance and Symmetric divergence, are\nused, and exponential and hinge loss penalties are adopted for the two measures\nrespectively. It is well known that the so-called \"multiplicative update rules\"\nresult in a much faster convergence than gradient descend for matrix\nfactorisation. However, applying such update rules to RPR-NMF and also proving\nits convergence is not straightforward. Thus, we use reasonable approximations\nto relax the complexity brought by the penalties, which are practically\nverified. Experiments on both synthetic datasets and real datasets demonstrate\nthat our algorithms have advantages on gaining close approximation, satisfying\na high proportion of expected constraints, and achieving superior performance\ncompared with other algorithms.","url_abs":"http://arxiv.org/abs/1803.02218v1","url_pdf":"http://arxiv.org/pdf/1803.02218v1.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":"relative-pairwise-relationship-constrained","repo_url":"https://github.com/shawn-jiang/RPRNMF","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"image-clustering","task_name":"Image Clustering"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"},{"task_slug":null,"task_name":"Triplet"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}