  In the light of regularized dynamic time warping kernels, this paper
re-considers the concept of time elastic centroid for a setof time series. We
derive a new algorithm based on a probabilistic interpretation of kernel
alignment matrices. This algorithm expressesthe averaging process in terms of a
stochastic alignment automata. It uses an iterative agglomerative heuristic
method for averagingthe aligned samples, while also averaging the times of
occurrence of the aligned samples. By comparing classification accuracies for45
heterogeneous time series datasets obtained by first nearest centroid/medoid
classifiers we show that: i) centroid-basedapproaches significantly outperform
medoid-based approaches, ii) for the considered datasets, our algorithm that
combines averagingin the sample space and along the time axes, emerges as the
most significantly robust model for time-elastic averaging with apromising
noise reduction capability. We also demonstrate its benefit in an isolated
gesture recognition experiment and its ability tosignificantly reduce the size
of training instance sets. Finally we highlight its denoising capability using
demonstrative synthetic data:we show that it is possible to retrieve, from few
noisy instances, a signal whose components are scattered in a wide spectral
band.
