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arXiv · 2006.12648

Aligning Time Series on Incomparable Spaces

Samuel Cohen·Giulia Luise·Alexander Terenin·Brandon Amos·Marc Peter Deisenroth
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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.

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Samuel Cohen, Giulia Luise, Alexander Terenin, Brandon Amos, Marc Peter Deisenroth. 2020-06-22. Aligning Time Series on Incomparable Spaces. https://arxiv.org/abs/2006.12648

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