{"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/on-application-of-block-kaczmarz-methods-in","title":"On Application of Block Kaczmarz Methods in Matrix Factorization","arxiv_id":"2010.10635","date":"2020-10-20","proceeding":null,"authors":["Edwin Chau","Jamie Haddock"],"abstract":"Matrix factorization techniques compute low-rank product approximations of high dimensional data matrices and as a result, are often employed in recommender systems and collaborative filtering applications. However, many algorithms for this task utilize an exact least-squares solver whose computation is time consuming and memory-expensive. In this paper we discuss and test a block Kaczmarz solver that replaces the least-squares subroutine in the common alternating scheme for matrix factorization. This variant trades a small increase in factorization error for significantly faster algorithmic performance. In doing so we find block sizes that produce a solution comparable to that of the least-squares solver for only a fraction of the runtime and working memory requirement.","url_abs":"https://arxiv.org/abs/2010.10635v1","url_pdf":"https://arxiv.org/pdf/2010.10635v1.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":"on-application-of-block-kaczmarz-methods-in","repo_url":"https://github.com/chaue/mf-algorithms","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"collaborative-filtering","task_name":"Collaborative Filtering"},{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"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}