{"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-dictionary-learning-optimal","title":"Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning","arxiv_id":"1708.01955","date":"2017-08-07","proceeding":null,"authors":["Morgan A. Schmitz","Matthieu Heitz","Nicolas Bonneel","Fred Maurice Ngolè Mboula","David Coeurjolly","Marco Cuturi","Gabriel Peyré","Jean-Luc Starck"],"abstract":"This paper introduces a new nonlinear dictionary learning method for\nhistograms in the probability simplex. The method leverages optimal transport\ntheory, in the sense that our aim is to reconstruct histograms using so-called\ndisplacement interpolations (a.k.a. Wasserstein barycenters) between dictionary\natoms; such atoms are themselves synthetic histograms in the probability\nsimplex. Our method simultaneously estimates such atoms, and, for each\ndatapoint, the vector of weights that can optimally reconstruct it as an\noptimal transport barycenter of such atoms. Our method is computationally\ntractable thanks to the addition of an entropic regularization to the usual\noptimal transportation problem, leading to an approximation scheme that is\nefficient, parallel and simple to differentiate. Both atoms and weights are\nlearned using a gradient-based descent method. Gradients are obtained by\nautomatic differentiation of the generalized Sinkhorn iterations that yield\nbarycenters with entropic smoothing. Because of its formulation relying on\nWasserstein barycenters instead of the usual matrix product between dictionary\nand codes, our method allows for nonlinear relationships between atoms and the\nreconstruction of input data. We illustrate its application in several\ndifferent image processing settings.","url_abs":"http://arxiv.org/abs/1708.01955v3","url_pdf":"http://arxiv.org/pdf/1708.01955v3.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-dictionary-learning-optimal","repo_url":"https://github.com/matthieuheitz/WassersteinDictionaryLearning","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"wasserstein-dictionary-learning-optimal","repo_url":"https://github.com/mark-fangzhou-xie/wigpy","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1708.01955","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}