{"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/high-dimensional-regularized-discriminant","title":"High-Dimensional Regularized Discriminant Analysis","arxiv_id":"1602.01182","date":"2016-02-03","proceeding":null,"authors":["John A. Ramey","Caleb K. Stein","Phil D. Young","Dean M. Young"],"abstract":"Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a\nwidely popular classifier that lacks interpretability and is impractical for\nhigh-dimensional data sets. Here, we present an interpretable and\ncomputationally efficient classifier called high-dimensional RDA (HDRDA),\ndesigned for the small-sample, high-dimensional setting. For HDRDA, we show\nthat each training observation, regardless of class, contributes to the class\ncovariance matrix, resulting in an interpretable estimator that borrows from\nthe pooled sample covariance matrix. Moreover, we show that HDRDA is equivalent\nto a classifier in a reduced-feature space with dimension approximately equal\nto the training sample size. As a result, the matrix operations employed by\nHDRDA are computationally linear in the number of features, making the\nclassifier well-suited for high-dimensional classification in practice. We\ndemonstrate that HDRDA is often superior to several sparse and regularized\nclassifiers in terms of classification accuracy with three artificial and six\nreal high-dimensional data sets. Also, timing comparisons between our HDRDA\nimplementation in the sparsediscrim R package and the standard RDA formulation\nin the klaR R package demonstrate that as the number of features increases, the\ncomputational runtime of HDRDA is drastically smaller than that of RDA.","url_abs":"http://arxiv.org/abs/1602.01182v2","url_pdf":"http://arxiv.org/pdf/1602.01182v2.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":"high-dimensional-regularized-discriminant","repo_url":"https://github.com/ramhiser/paper-hdrda","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[{"method_slug":"interpretability","method_name":"Interpretability"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}