{"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/efficient-robust-optimal-transport","title":"Efficient Robust Optimal Transport with Application to Multi-Label Classification","arxiv_id":"2010.11852","date":"2020-10-22","proceeding":null,"authors":["Pratik Jawanpuria","N T V Satyadev","Bamdev Mishra"],"abstract":"Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account while learning the transport plan between two distributions. We model the feature-feature relationship via a symmetric positive semi-definite Mahalanobis metric in the OT cost function. For a certain class of regularizers on the metric, we show that the optimization strategy can be considerably simplified by exploiting the problem structure. For high-dimensional data, we additionally propose suitable low-dimensional modeling of the Mahalanobis metric. Overall, we view the resulting optimization problem as a non-linear OT problem, which we solve using the Frank-Wolfe algorithm. Empirical results on the discriminative learning setting, such as tag prediction and multi-class classification, illustrate the good performance of our approach.","url_abs":"https://arxiv.org/abs/2010.11852v2","url_pdf":"https://arxiv.org/pdf/2010.11852v2.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":"efficient-robust-optimal-transport","repo_url":"https://github.com/SatyadevNtv/ROT4C","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"efficient-robust-optimal-transport","repo_url":"https://github.com/satyadevntv/ROT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"multi-label-classification-2","task_name":"MUlTI-LABEL-ClASSIFICATION"},{"task_slug":"multi-label-classification","task_name":"Multi-Label Classification"},{"task_slug":"multi-class-classification","task_name":"Multi-class Classification"},{"task_slug":"tag","task_name":"TAG"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2010.11852","atlas_url":"https://app.syntology.ai/?focus=2010.11852","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}