{"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/preconditioned-data-sparsification-for-big","title":"Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means","arxiv_id":"1511.00152","date":"2015-10-31","proceeding":null,"authors":["Farhad Pourkamali-Anaraki","Stephen Becker"],"abstract":"We analyze a compression scheme for large data sets that randomly keeps a\nsmall percentage of the components of each data sample. The benefit is that the\noutput is a sparse matrix and therefore subsequent processing, such as PCA or\nK-means, is significantly faster, especially in a distributed-data setting.\nFurthermore, the sampling is single-pass and applicable to streaming data. The\nsampling mechanism is a variant of previous methods proposed in the literature\ncombined with a randomized preconditioning to smooth the data. We provide\nguarantees for PCA in terms of the covariance matrix, and guarantees for\nK-means in terms of the error in the center estimators at a given step. We\npresent numerical evidence to show both that our bounds are nearly tight and\nthat our algorithms provide a real benefit when applied to standard test data\nsets, as well as providing certain benefits over related sampling approaches.","url_abs":"http://arxiv.org/abs/1511.00152v3","url_pdf":"http://arxiv.org/pdf/1511.00152v3.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":"preconditioned-data-sparsification-for-big","repo_url":"https://github.com/stephenbeckr/SparsifiedKMeans","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"preconditioned-data-sparsification-for-big","repo_url":"https://github.com/erickightley/sparseklearn","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}