{"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/geometric-mean-metric-learning","title":"Geometric Mean Metric Learning","arxiv_id":"1607.05002","date":"2016-07-18","proceeding":null,"authors":["Pourya Habib Zadeh","Reshad Hosseini","Suvrit Sra"],"abstract":"We revisit the task of learning a Euclidean metric from data. We approach\nthis problem from first principles and formulate it as a surprisingly simple\noptimization problem. Indeed, our formulation even admits a closed form\nsolution. This solution possesses several very attractive properties: (i) an\ninnate geometric appeal through the Riemannian geometry of positive definite\nmatrices; (ii) ease of interpretability; and (iii) computational speed several\norders of magnitude faster than the widely used LMNN and ITML methods.\nFurthermore, on standard benchmark datasets, our closed-form solution\nconsistently attains higher classification accuracy.","url_abs":"http://arxiv.org/abs/1607.05002v1","url_pdf":"http://arxiv.org/pdf/1607.05002v1.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":"geometric-mean-metric-learning","repo_url":"https://github.com/PouriaZ/GMML","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"form","task_name":"Form"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"metric-learning","task_name":"Metric Learning"},{"task_slug":"riemannian-optimization","task_name":"Riemannian optimization"}],"methods":[{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1607.05002","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}