{"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/applicability-and-interpretation-of-the","title":"Applicability and interpretation of the deterministic weighted cepstral distance","arxiv_id":"1803.03104","date":"2018-03-08","proceeding":null,"authors":["Oliver Lauwers","Bart De Moor"],"abstract":"Quantifying similarity between data objects is an important part of modern\ndata science. Deciding what similarity measure to use is very application\ndependent. In this paper, we combine insights from systems theory and machine\nlearning, and investigate the weighted cepstral distance, which was previously\ndefined for signals coming from ARMA models. We provide an extension of this\ndistance to invertible deterministic linear time invariant single input single\noutput models, and assess its applicability. We show that it can always be\ninterpreted in terms of the poles and zeros of the underlying model, and that,\nin the case of stable, minimum-phase, or unstable, maximum-phase models, a\ngeometrical interpretation in terms of subspace angles can be given. We then\ndevise a method to assess stability and phase-type of the generating models,\nusing only input/output signal information. In this way, we prove a connection\nbetween the extended weighted cepstral distance and a weighted cepstral model\nnorm. In this way, we provide a purely data-driven way to assess different\nunderlying dynamics of input/output signal pairs, without the need for any\nsystem identification step. This can be useful in machine learning tasks such\nas time series clustering. An iPython tutorial is published complementary to\nthis paper, containing implementations of the various methods and algorithms\npresented here, as well as some numerical illustrations of the equivalences\nproven here.","url_abs":"http://arxiv.org/abs/1803.03104v1","url_pdf":"http://arxiv.org/pdf/1803.03104v1.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":"applicability-and-interpretation-of-the","repo_url":"https://github.com/Olauwers/Applicability-and-interpretation-of-the-deterministic-weighted-cepstral-distance","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"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":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}