{"title":"Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions","_id":"16293","department":[{"_id":"101"}],"user_id":"47427","citation":{"apa":"Klus, S., Peitz, S., &#38; Schuster, I. (2018). Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions. <i>ArXiv:1805.10118</i>.","mla":"Klus, Stefan, et al. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer  Operator Eigenfunctions.” <i>ArXiv:1805.10118</i>, 2018.","ama":"Klus S, Peitz S, Schuster I. Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions. <i>arXiv:180510118</i>. 2018.","ieee":"S. Klus, S. Peitz, and I. Schuster, “Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions,” <i>arXiv:1805.10118</i>. 2018.","chicago":"Klus, Stefan, Sebastian Peitz, and Ingmar Schuster. “Analyzing High-Dimensional Time-Series Data Using Kernel Transfer  Operator Eigenfunctions.” <i>ArXiv:1805.10118</i>, 2018.","short":"S. Klus, S. Peitz, I. Schuster, ArXiv:1805.10118 (2018).","bibtex":"@article{Klus_Peitz_Schuster_2018, title={Analyzing high-dimensional time-series data using kernel transfer  operator eigenfunctions}, journal={arXiv:1805.10118}, author={Klus, Stefan and Peitz, Sebastian and Schuster, Ingmar}, year={2018} }"},"date_created":"2020-03-13T12:44:12Z","status":"public","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"year":"2018","abstract":[{"lang":"eng","text":"Kernel transfer operators, which can be regarded as approximations of\r\ntransfer operators such as the Perron-Frobenius or Koopman operator in\r\nreproducing kernel Hilbert spaces, are defined in terms of covariance and\r\ncross-covariance operators and have been shown to be closely related to the\r\nconditional mean embedding framework developed by the machine learning\r\ncommunity. The goal of this paper is to show how the dominant eigenfunctions of\r\nthese operators in combination with gradient-based optimization techniques can\r\nbe used to detect long-lived coherent patterns in high-dimensional time-series\r\ndata. The results will be illustrated using video data and a fluid flow\r\nexample."}],"author":[{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz"},{"full_name":"Schuster, Ingmar","last_name":"Schuster","first_name":"Ingmar"}],"oa":"1","date_updated":"2022-01-06T06:52:48Z","type":"preprint","publication":"arXiv:1805.10118","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/1805.10118.pdf"}]}