{"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/k-means-on-a-log-cholesky-manifold-with","title":"$k$-means on Positive Definite Matrices, and an Application to Clustering in Radar Image Sequences","arxiv_id":"2008.03454","date":"2020-08-08","proceeding":null,"authors":["Daniel Fryer","Hien Nguyen","Pascal Castellazzi"],"abstract":"We state theoretical properties for $k$-means clustering of Symmetric Positive Definite (SPD) matrices, in a non-Euclidean space, that provides a natural and favourable representation of these data. We then provide a novel application for this method, to time-series clustering of pixels in a sequence of Synthetic Aperture Radar images, via their finite-lag autocovariance matrices.","url_abs":"https://arxiv.org/abs/2008.03454v2","url_pdf":"https://arxiv.org/pdf/2008.03454v2.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":"k-means-on-a-log-cholesky-manifold-with","repo_url":"https://github.com/frycast/kmspd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"time-series-clustering","task_name":"Time Series Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}