{"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/metric-on-nonlinear-dynamical-systems-with","title":"Metric on Nonlinear Dynamical Systems with Perron-Frobenius Operators","arxiv_id":"1805.12324","date":"2018-05-31","proceeding":"NeurIPS 2018 12","authors":["Isao Ishikawa","Keisuke Fujii","Masahiro Ikeda","Yuka Hashimoto","Yoshinobu Kawahara"],"abstract":"The development of a metric for structural data is a long-term problem in\npattern recognition and machine learning. In this paper, we develop a general\nmetric for comparing nonlinear dynamical systems that is defined with\nPerron-Frobenius operators in reproducing kernel Hilbert spaces. Our metric\nincludes the existing fundamental metrics for dynamical systems, which are\nbasically defined with principal angles between some appropriately-chosen\nsubspaces, as its special cases. We also describe the estimation of our metric\nfrom finite data. We empirically illustrate our metric with an example of\nrotation dynamics in a unit disk in a complex plane, and evaluate the\nperformance with real-world time-series data.","url_abs":"http://arxiv.org/abs/1805.12324v2","url_pdf":"http://arxiv.org/pdf/1805.12324v2.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":"metric-on-nonlinear-dynamical-systems-with","repo_url":"https://github.com/keisuke198619/metricNLDS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"metric-on-nonlinear-dynamical-systems-with","repo_url":"https://github.com/ooblahman/koopman-robust-control","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1805.12324","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}