{"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/random-matrix-theory-improved-frechet-mean-of","title":"Random matrix theory improved Fréchet mean of symmetric positive definite matrices","arxiv_id":"2405.06558","date":"2024-05-10","proceeding":null,"authors":["Florent Bouchard","Ammar Mian","Malik Tiomoko","Guillaume Ginolhac","Frédéric Pascal"],"abstract":"In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine-learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory-based method that estimates Fr\\'echet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.","url_abs":"https://arxiv.org/abs/2405.06558v2","url_pdf":"https://arxiv.org/pdf/2405.06558v2.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":"random-matrix-theory-improved-frechet-mean-of","repo_url":"https://github.com/ammarmian/icml-rmt-2024","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"eeg-1","task_name":"EEG"}],"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}