Aligning Time Series on Incomparable Spaces
Samuel Cohen, Giulia Luise, Alexander Terenin, Brandon Amos, Marc Deisenroth
Abstract
Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning.
BibTeX
@InProceedings{pmlr-v130-cohen21a,
title = { Aligning Time Series on Incomparable Spaces },
author = {Cohen, Samuel and Luise, Giulia and Terenin, Alexander and Amos, Brandon and Deisenroth, Marc},
booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
pages = {1036--1044},
year = {2021},
editor = {Banerjee, Arindam and Fukumizu, Kenji},
volume = {130},
series = {Proceedings of Machine Learning Research},
month = {13--15 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v130/cohen21a/cohen21a.pdf},
url = {https://proceedings.mlr.press/v130/cohen21a.html},
abstract = { Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning. }
}