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Paper details
Number 2 - June 2019
Volume 29 - 2019
Times series averaging and denoising from a probabilistic perspective on time-elastic kernels
Pierre-Francois Marteau
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.
Keywords
time series averaging, time elastic kernel, dynamic time warping, hidden Markov model, classification, denoising