{"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/generalized-low-rank-models","title":"Generalized Low Rank Models","arxiv_id":"1410.0342","date":"2014-10-01","proceeding":null,"authors":["Madeleine Udell","Corinne Horn","Reza Zadeh","Stephen Boyd"],"abstract":"Principal components analysis (PCA) is a well-known technique for\napproximating a tabular data set by a low rank matrix. Here, we extend the idea\nof PCA to handle arbitrary data sets consisting of numerical, Boolean,\ncategorical, ordinal, and other data types. This framework encompasses many\nwell known techniques in data analysis, such as nonnegative matrix\nfactorization, matrix completion, sparse and robust PCA, $k$-means, $k$-SVD,\nand maximum margin matrix factorization. The method handles heterogeneous data\nsets, and leads to coherent schemes for compressing, denoising, and imputing\nmissing entries across all data types simultaneously. It also admits a number\nof interesting interpretations of the low rank factors, which allow clustering\nof examples or of features. We propose several parallel algorithms for fitting\ngeneralized low rank models, and describe implementations and numerical\nresults.","url_abs":"http://arxiv.org/abs/1410.0342v4","url_pdf":"http://arxiv.org/pdf/1410.0342v4.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":"generalized-low-rank-models","repo_url":"https://github.com/madeleineudell/LowRankModels.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"matrix-completion","task_name":"Matrix Completion"}],"methods":[{"method_slug":"pca","method_name":"PCA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1410.0342","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}