{"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/sinkhorn-divergence-of-topological-signature","title":"Sinkhorn Divergence of Topological Signature Estimates for Time Series Classification","arxiv_id":"1902.05326","date":"2019-02-14","proceeding":null,"authors":["Colin Stephen"],"abstract":"Distinguishing between classes of time series sampled from dynamic systems is\na common challenge in systems and control engineering, for example in the\ncontext of health monitoring, fault detection, and quality control. The\nchallenge is increased when no underlying model of a system is known,\nmeasurement noise is present, and long signals need to be interpreted. In this\npaper we address these issues with a new non parametric classifier based on\ntopological signatures. Our model learns classes as weighted kernel density\nestimates (KDEs) over persistent homology diagrams and predicts new trajectory\nlabels using Sinkhorn divergences on the space of diagram KDEs to quantify\nproximity. We show that this approach accurately discriminates between states\nof chaotic systems that are close in parameter space, and its performance is\nrobust to noise.","url_abs":"http://arxiv.org/abs/1902.05326v1","url_pdf":"http://arxiv.org/pdf/1902.05326v1.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":"sinkhorn-divergence-of-topological-signature","repo_url":"https://github.com/colinstephen/icmla2018","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"fault-detection","task_name":"Fault Detection"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"time-series-classification","task_name":"Time Series Classification"}],"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}