Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels
In the light of regularized dynamic time warping kernels, this paper re-considers the concept of a time elastic centroid for a set of time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices. This algorithm expresses the averaging process in terms o...
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| Format: | Article |
| Language: | English |
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Sciendo
2019-06-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.2478/amcs-2019-0028 |
| _version_ | 1831590816113491968 |
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| author | Marteau Pierre-Francois |
| author_facet | Marteau Pierre-Francois |
| author_sort | Marteau Pierre-Francois |
| collection | DOAJ |
| description | In the light of regularized dynamic time warping kernels, this paper re-considers the concept of a time elastic centroid for a set of time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices. This algorithm expresses the averaging process in terms of stochastic alignment automata. It uses an iterative agglomerative heuristic method for averaging the aligned samples, while also averaging the times of their occurrence. By comparing classification accuracies for 45 heterogeneous time series data sets obtained by first nearest centroid/medoid classifiers, we show that (i) centroid-based approaches significantly outperform medoid-based ones, (ii) for the data sets considered, our algorithm, which combines averaging in the sample space and along the time axes, emerges as the most significantly robust model for time-elastic averaging with a promising noise reduction capability. We also demonstrate its benefit in an isolated gesture recognition experiment and its ability to significantly reduce the size of training instance sets. Finally, we highlight its denoising capability using demonstrative synthetic data. Specifically, we show that it is possible to retrieve, from few noisy instances, a signal whose components are scattered in a wide spectral band. |
| first_indexed | 2024-12-18T01:12:43Z |
| format | Article |
| id | doaj.art-9b19d6ac012e41a5914f6931a4da1754 |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-18T01:12:43Z |
| publishDate | 2019-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-9b19d6ac012e41a5914f6931a4da17542022-12-21T21:26:03ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922019-06-0129237539210.2478/amcs-2019-0028amcs-2019-0028Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic KernelsMarteau Pierre-Francois0Institute for Research in Computer Science and Stochastic Systems (IRISA), University of Southern Brittany, Tohannic Campus, 56000Vannes, FranceIn the light of regularized dynamic time warping kernels, this paper re-considers the concept of a time elastic centroid for a set of time series. We derive a new algorithm based on a probabilistic interpretation of kernel alignment matrices. This algorithm expresses the averaging process in terms of stochastic alignment automata. It uses an iterative agglomerative heuristic method for averaging the aligned samples, while also averaging the times of their occurrence. By comparing classification accuracies for 45 heterogeneous time series data sets obtained by first nearest centroid/medoid classifiers, we show that (i) centroid-based approaches significantly outperform medoid-based ones, (ii) for the data sets considered, our algorithm, which combines averaging in the sample space and along the time axes, emerges as the most significantly robust model for time-elastic averaging with a promising noise reduction capability. We also demonstrate its benefit in an isolated gesture recognition experiment and its ability to significantly reduce the size of training instance sets. Finally, we highlight its denoising capability using demonstrative synthetic data. Specifically, we show that it is possible to retrieve, from few noisy instances, a signal whose components are scattered in a wide spectral band.https://doi.org/10.2478/amcs-2019-0028time series averagingtime elastic kerneldynamic time warpinghidden markov modelclassificationdenoising |
| spellingShingle | Marteau Pierre-Francois Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels International Journal of Applied Mathematics and Computer Science time series averaging time elastic kernel dynamic time warping hidden markov model classification denoising |
| title | Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels |
| title_full | Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels |
| title_fullStr | Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels |
| title_full_unstemmed | Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels |
| title_short | Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels |
| title_sort | times series averaging and denoising from a probabilistic perspective on time elastic kernels |
| topic | time series averaging time elastic kernel dynamic time warping hidden markov model classification denoising |
| url | https://doi.org/10.2478/amcs-2019-0028 |
| work_keys_str_mv | AT marteaupierrefrancois timesseriesaveraginganddenoisingfromaprobabilisticperspectiveontimeelastickernels |