Disentangling dynamic and stochastic modes in multivariate time series
A signal decomposition is presented that disentangles the deterministic and stochastic components of a multivariate time series. The dynamical component analysis (DyCA) algorithm is based on the assumption that an unknown set of ordinary differential equations (ODEs) describes the dynamics of the de...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2024-10-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2024.1456635/full |
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| author | Christian Uhl Annika Stiehl Nicolas Weeger Markus Schlarb Markus Schlarb Knut Hüper |
| author_facet | Christian Uhl Annika Stiehl Nicolas Weeger Markus Schlarb Markus Schlarb Knut Hüper |
| author_sort | Christian Uhl |
| collection | DOAJ |
| description | A signal decomposition is presented that disentangles the deterministic and stochastic components of a multivariate time series. The dynamical component analysis (DyCA) algorithm is based on the assumption that an unknown set of ordinary differential equations (ODEs) describes the dynamics of the deterministic part of the signal. The algorithm is thoroughly derived and accompanied by a link to the GitHub repository containing the algorithm. The method was applied to both simulated and real-world data sets and compared to the results of principal component analysis (PCA), independent component analysis (ICA), and dynamic mode decomposition (DMD). The results demonstrate that DyCA is capable of separating the deterministic and stochastic components of the signal. Furthermore, the algorithm is able to estimate the number of linear and non-linear differential equations and to extract the corresponding amplitudes. The results demonstrate that DyCA is an effective tool for signal decomposition and dimension reduction of multivariate time series. In this regard, DyCA outperforms PCA and ICA and is on par or slightly superior to the DMD algorithm in terms of performance. |
| format | Article |
| id | doaj-art-534ae9ce2fb946a099fd2a8a0db4b29a |
| institution | OA Journals |
| issn | 2297-4687 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-534ae9ce2fb946a099fd2a8a0db4b29a2025-08-20T02:08:45ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872024-10-011010.3389/fams.2024.14566351456635Disentangling dynamic and stochastic modes in multivariate time seriesChristian Uhl0Annika Stiehl1Nicolas Weeger2Markus Schlarb3Markus Schlarb4Knut Hüper5Center for Signal Analysis of Complex Systems, Ansbach University of Applied Sciences, Ansbach, GermanyCenter for Signal Analysis of Complex Systems, Ansbach University of Applied Sciences, Ansbach, GermanyCenter for Signal Analysis of Complex Systems, Ansbach University of Applied Sciences, Ansbach, GermanyCenter for Signal Analysis of Complex Systems, Ansbach University of Applied Sciences, Ansbach, GermanyInstitute of Mathematics, Julius-Maximilians-Universität, Würzburg, GermanyInstitute of Mathematics, Julius-Maximilians-Universität, Würzburg, GermanyA signal decomposition is presented that disentangles the deterministic and stochastic components of a multivariate time series. The dynamical component analysis (DyCA) algorithm is based on the assumption that an unknown set of ordinary differential equations (ODEs) describes the dynamics of the deterministic part of the signal. The algorithm is thoroughly derived and accompanied by a link to the GitHub repository containing the algorithm. The method was applied to both simulated and real-world data sets and compared to the results of principal component analysis (PCA), independent component analysis (ICA), and dynamic mode decomposition (DMD). The results demonstrate that DyCA is capable of separating the deterministic and stochastic components of the signal. Furthermore, the algorithm is able to estimate the number of linear and non-linear differential equations and to extract the corresponding amplitudes. The results demonstrate that DyCA is an effective tool for signal decomposition and dimension reduction of multivariate time series. In this regard, DyCA outperforms PCA and ICA and is on par or slightly superior to the DMD algorithm in terms of performance.https://www.frontiersin.org/articles/10.3389/fams.2024.1456635/fulldynamical component analysis (DyCA)dynamic mode decomposition (DMD)dimension reductiondynamical systemsblind source separationdifferential equations |
| spellingShingle | Christian Uhl Annika Stiehl Nicolas Weeger Markus Schlarb Markus Schlarb Knut Hüper Disentangling dynamic and stochastic modes in multivariate time series Frontiers in Applied Mathematics and Statistics dynamical component analysis (DyCA) dynamic mode decomposition (DMD) dimension reduction dynamical systems blind source separation differential equations |
| title | Disentangling dynamic and stochastic modes in multivariate time series |
| title_full | Disentangling dynamic and stochastic modes in multivariate time series |
| title_fullStr | Disentangling dynamic and stochastic modes in multivariate time series |
| title_full_unstemmed | Disentangling dynamic and stochastic modes in multivariate time series |
| title_short | Disentangling dynamic and stochastic modes in multivariate time series |
| title_sort | disentangling dynamic and stochastic modes in multivariate time series |
| topic | dynamical component analysis (DyCA) dynamic mode decomposition (DMD) dimension reduction dynamical systems blind source separation differential equations |
| url | https://www.frontiersin.org/articles/10.3389/fams.2024.1456635/full |
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