{"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/wasserstein-discriminant-analysis","title":"Wasserstein Discriminant Analysis","arxiv_id":"1608.08063","date":"2016-08-29","proceeding":null,"authors":["Rémi Flamary","Marco Cuturi","Nicolas Courty","Alain Rakotomamonjy"],"abstract":"Wasserstein Discriminant Analysis (WDA) is a new supervised method that can\nimprove classification of high-dimensional data by computing a suitable linear\nmap onto a lower dimensional subspace. Following the blueprint of classical\nLinear Discriminant Analysis (LDA), WDA selects the projection matrix that\nmaximizes the ratio of two quantities: the dispersion of projected points\ncoming from different classes, divided by the dispersion of projected points\ncoming from the same class. To quantify dispersion, WDA uses regularized\nWasserstein distances, rather than cross-variance measures which have been\nusually considered, notably in LDA. Thanks to the the underlying principles of\noptimal transport, WDA is able to capture both global (at distribution scale)\nand local (at samples scale) interactions between classes. Regularized\nWasserstein distances can be computed using the Sinkhorn matrix scaling\nalgorithm; We show that the optimization of WDA can be tackled using automatic\ndifferentiation of Sinkhorn iterations. Numerical experiments show promising\nresults both in terms of prediction and visualization on toy examples and real\nlife datasets such as MNIST and on deep features obtained from a subset of the\nCaltech dataset.","url_abs":"http://arxiv.org/abs/1608.08063v2","url_pdf":"http://arxiv.org/pdf/1608.08063v2.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":"wasserstein-discriminant-analysis","repo_url":"https://github.com/rflamary/POT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"lda","method_name":"LDA"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1608.08063","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}