{"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/a-unified-parallel-algorithm-for-regularized","title":"A Unified Parallel Algorithm for Regularized Group PLS Scalable to Big Data","arxiv_id":"1702.07066","date":"2017-02-23","proceeding":null,"authors":["Pierre Lafaye de Micheaux","Benoit Liquet","Matthew Sutton"],"abstract":"Partial Least Squares (PLS) methods have been heavily exploited to analyse\nthe association between two blocs of data. These powerful approaches can be\napplied to data sets where the number of variables is greater than the number\nof observations and in presence of high collinearity between variables.\nDifferent sparse versions of PLS have been developed to integrate multiple data\nsets while simultaneously selecting the contributing variables. Sparse\nmodelling is a key factor in obtaining better estimators and identifying\nassociations between multiple data sets. The cornerstone of the sparsity\nversion of PLS methods is the link between the SVD of a matrix (constructed\nfrom deflated versions of the original matrices of data) and least squares\nminimisation in linear regression. We present here an accurate description of\nthe most popular PLS methods, alongside their mathematical proofs. A unified\nalgorithm is proposed to perform all four types of PLS including their\nregularised versions. Various approaches to decrease the computation time are\noffered, and we show how the whole procedure can be scalable to big data sets.","url_abs":"http://arxiv.org/abs/1702.07066v1","url_pdf":"http://arxiv.org/pdf/1702.07066v1.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":"a-unified-parallel-algorithm-for-regularized","repo_url":"https://github.com/matt-sutton/bigsgPLS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"mathematical-proofs","task_name":"Mathematical Proofs"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}