{"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/a-unified-framework-for-domain-adaptation","title":"A Unified Framework for Domain Adaptation using Metric Learning on Manifolds","arxiv_id":"1804.10834","date":"2018-04-28","proceeding":null,"authors":["Sridhar Mahadevan","Bamdev Mishra","Shalini Ghosh"],"abstract":"We present a novel framework for domain adaptation, whereby both geometric\nand statistical differences between a labeled source domain and unlabeled\ntarget domain can be integrated by exploiting the curved Riemannian geometry of\nstatistical manifolds. Our approach is based on formulating transfer from\nsource to target as a problem of geometric mean metric learning on manifolds.\nSpecifically, we exploit the curved Riemannian manifold geometry of symmetric\npositive definite (SPD) covariance matrices. We exploit a simple but important\nobservation that as the space of covariance matrices is both a Riemannian space\nas well as a homogeneous space, the shortest path geodesic between two\ncovariances on the manifold can be computed analytically. Statistics on the SPD\nmatrix manifold, such as the geometric mean of two matrices can be reduced to\nsolving the well-known Riccati equation. We show how the Ricatti-based solution\ncan be constrained to not only reduce the statistical differences between the\nsource and target domains, such as aligning second order covariances and\nminimizing the maximum mean discrepancy, but also the underlying geometry of\nthe source and target domains using diffusions on the underlying source and\ntarget manifolds. A key strength of our proposed approach is that it enables\nintegrating multiple sources of variation between source and target in a\nunified way, by reducing the combined objective function to a nested set of\nRicatti equations where the solution can be represented by a cascaded series of\ngeometric mean computations. In addition to showing the theoretical optimality\nof our solution, we present detailed experiments using standard transfer\nlearning testbeds from computer vision comparing our proposed algorithms to\npast work in domain adaptation, showing improved results over a large variety\nof previous methods.","url_abs":"http://arxiv.org/abs/1804.10834v1","url_pdf":"http://arxiv.org/pdf/1804.10834v1.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":"a-unified-framework-for-domain-adaptation","repo_url":"https://github.com/sridharmahadevan/Geodesic-Covariance-Alignment","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"domain-adaptation","task_name":"Domain Adaptation"},{"task_slug":"metric-learning","task_name":"Metric Learning"},{"task_slug":"transfer-learning","task_name":"Transfer Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.10834","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}