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Smoothing method for unit quaternion time series in a classification problem: an application to motion data

Smoothing orientation data is a fundamental task in different fields of research. Different methods of smoothing time series in quaternion algebras have been described in the literature, but their application is still an open point. This paper develops a smoothing approach for smoothing quaternion t...

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Detalles Bibliográficos
Autores principales: Ballante, Elena, Bellanger, Lise, Drouin, Pierre, Figini, Silvia, Stamm, Aymeric
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10256761/
https://www.ncbi.nlm.nih.gov/pubmed/37296200
http://dx.doi.org/10.1038/s41598-023-36480-y
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author Ballante, Elena
Bellanger, Lise
Drouin, Pierre
Figini, Silvia
Stamm, Aymeric
author_facet Ballante, Elena
Bellanger, Lise
Drouin, Pierre
Figini, Silvia
Stamm, Aymeric
author_sort Ballante, Elena
collection PubMed
description Smoothing orientation data is a fundamental task in different fields of research. Different methods of smoothing time series in quaternion algebras have been described in the literature, but their application is still an open point. This paper develops a smoothing approach for smoothing quaternion time series to obtain good performance in classification problems. Starting from an existing method which involves an angular velocity transformation of unit quaternion time series, a new method which employ the logarithm function to transform the quaternion time series to a real three-dimensional time series is proposed. Empirical evidences achieved on real data set and artificially noisy data sets confirm the effectiveness of the proposed method compared with the classical approach based on angular velocity transformation. The R functions developed for this paper will be provided in a Github repository.
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spelling pubmed-102567612023-06-11 Smoothing method for unit quaternion time series in a classification problem: an application to motion data Ballante, Elena Bellanger, Lise Drouin, Pierre Figini, Silvia Stamm, Aymeric Sci Rep Article Smoothing orientation data is a fundamental task in different fields of research. Different methods of smoothing time series in quaternion algebras have been described in the literature, but their application is still an open point. This paper develops a smoothing approach for smoothing quaternion time series to obtain good performance in classification problems. Starting from an existing method which involves an angular velocity transformation of unit quaternion time series, a new method which employ the logarithm function to transform the quaternion time series to a real three-dimensional time series is proposed. Empirical evidences achieved on real data set and artificially noisy data sets confirm the effectiveness of the proposed method compared with the classical approach based on angular velocity transformation. The R functions developed for this paper will be provided in a Github repository. Nature Publishing Group UK 2023-06-09 /pmc/articles/PMC10256761/ /pubmed/37296200 http://dx.doi.org/10.1038/s41598-023-36480-y Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Ballante, Elena
Bellanger, Lise
Drouin, Pierre
Figini, Silvia
Stamm, Aymeric
Smoothing method for unit quaternion time series in a classification problem: an application to motion data
title Smoothing method for unit quaternion time series in a classification problem: an application to motion data
title_full Smoothing method for unit quaternion time series in a classification problem: an application to motion data
title_fullStr Smoothing method for unit quaternion time series in a classification problem: an application to motion data
title_full_unstemmed Smoothing method for unit quaternion time series in a classification problem: an application to motion data
title_short Smoothing method for unit quaternion time series in a classification problem: an application to motion data
title_sort smoothing method for unit quaternion time series in a classification problem: an application to motion data
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10256761/
https://www.ncbi.nlm.nih.gov/pubmed/37296200
http://dx.doi.org/10.1038/s41598-023-36480-y
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