{"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/times-series-averaging-and-denoising-from-a","title":"Times series averaging and denoising from a probabilistic perspective on time-elastic kernels","arxiv_id":"1611.09194","date":"2016-11-28","proceeding":null,"authors":["Pierre-François Marteau"],"abstract":"In the light of regularized dynamic time warping kernels, this paper\nre-considers the concept of time elastic centroid for a setof time series. We\nderive a new algorithm based on a probabilistic interpretation of kernel\nalignment matrices. This algorithm expressesthe averaging process in terms of a\nstochastic alignment automata. It uses an iterative agglomerative heuristic\nmethod for averagingthe aligned samples, while also averaging the times of\noccurrence of the aligned samples. By comparing classification accuracies for45\nheterogeneous time series datasets obtained by first nearest centroid/medoid\nclassifiers we show that: i) centroid-basedapproaches significantly outperform\nmedoid-based approaches, ii) for the considered datasets, our algorithm that\ncombines averagingin the sample space and along the time axes, emerges as the\nmost significantly robust model for time-elastic averaging with apromising\nnoise reduction capability. We also demonstrate its benefit in an isolated\ngesture recognition experiment and its ability tosignificantly reduce the size\nof training instance sets. Finally we highlight its denoising capability using\ndemonstrative synthetic data:we show that it is possible to retrieve, from few\nnoisy instances, a signal whose components are scattered in a wide spectral\nband.","url_abs":"http://arxiv.org/abs/1611.09194v4","url_pdf":"http://arxiv.org/pdf/1611.09194v4.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":"times-series-averaging-and-denoising-from-a","repo_url":"https://github.com/pfmarteau/ShapeTimeSeparation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"times-series-averaging-and-denoising-from-a","repo_url":"https://github.com/pfmarteau/eKATS","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"dynamic-time-warping","task_name":"Dynamic Time Warping"},{"task_slug":"gesture-recognition","task_name":"Gesture Recognition"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"},{"task_slug":"time-series-denoising","task_name":"Time Series Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}