Aligning Time Series on Incomparable Spaces

Samuel Cohen, Giulia Luise, Alexander Terenin, Brandon Amos, Marc Deisenroth
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1036-1044, 2021.

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.

Cite this Paper

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. } }
Endnote
%0 Conference Paper %T Aligning Time Series on Incomparable Spaces %A Samuel Cohen %A Giulia Luise %A Alexander Terenin %A Brandon Amos %A Marc Deisenroth %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-cohen21a %I PMLR %P 1036--1044 %U https://proceedings.mlr.press/v130/cohen21a.html %V 130 %X 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.
APA
Cohen, S., Luise, G., Terenin, A., Amos, B. & Deisenroth, M.. (2021). Aligning Time Series on Incomparable Spaces . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1036-1044 Available from https://proceedings.mlr.press/v130/cohen21a.html.

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