{"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/correlation-alignment-by-riemannian-metric","title":"Correlation Alignment by Riemannian Metric for Domain Adaptation","arxiv_id":"1705.08180","date":"2017-05-23","proceeding":null,"authors":["Pietro Morerio","Vittorio Murino"],"abstract":"Domain adaptation techniques address the problem of reducing the sensitivity\nof machine learning methods to the so-called domain shift, namely the\ndifference between source (training) and target (test) data distributions. In\nparticular, unsupervised domain adaptation assumes no labels are available in\nthe target domain. To this end, aligning second order statistics (covariances)\nof target and source domains have proven to be an effective approach ti fill\nthe gap between the domains. However, covariance matrices do not form a\nsubspace of the Euclidean space, but live in a Riemannian manifold with\nnon-positive curvature, making the usual Euclidean metric suboptimal to measure\ndistances. In this paper, we extend the idea of training a neural network with\na constraint on the covariances of the hidden layer features, by rigorously\naccounting for the curved structure of the manifold of symmetric positive\ndefinite matrices. The resulting loss function exploits a theoretically sound\ngeodesic distance on such manifold. Results show indeed the suboptimal nature\nof the Euclidean distance. This makes us able to perform better than previous\napproaches on the standard Office dataset, a benchmark for domain adaptation\ntechniques.","url_abs":"http://arxiv.org/abs/1705.08180v1","url_pdf":"http://arxiv.org/pdf/1705.08180v1.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":"correlation-alignment-by-riemannian-metric","repo_url":"https://github.com/lzx6/deep-coral","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"domain-adaptation","task_name":"Domain Adaptation"},{"task_slug":"unsupervised-domain-adaptation","task_name":"Unsupervised Domain Adaptation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}