<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>automata</italic>. 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.</p></abstract>

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.

Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels

Institute for Research in Computer Science and Stochastic Systems (IRISA)

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels

Published Online: Jul 04, 2019

Page range: 375 - 392

Received: Jul 08, 2018

Accepted: Oct 23, 2018

DOI: https://doi.org/10.2478/amcs-2019-0028

Keywords
time series averaging, time elastic kernel, dynamic time warping, hidden Markov model, classification, denoising

© 2019 Pierre-Francois Marteau, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels

Published Online: Jul 04, 2019

Page range: 375 - 392

Received: Jul 08, 2018

Accepted: Oct 23, 2018

DOI: https://doi.org/10.2478/amcs-2019-0028

Keywordstime series averaging, time elastic kernel, dynamic time warping, hidden Markov model, classification, denoising

© 2019 Pierre-Francois Marteau, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
time series averaging, time elastic kernel, dynamic time warping, hidden Markov model, classification, denoising