Aligning Time Series on Incomparable Spaces

• URL: http://arxiv.org/abs/2006.12648v2
• Date: Mon, 22 Feb 2021 19:33:03 GMT
• Title: Aligning Time Series on Incomparable Spaces
• Authors: Samuel Cohen, Giulia Luise, Alexander Terenin, Brandon Amos, Marc Peter Deisenroth
• Abstract summary: We propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces.
• Score: 83.8261699057419
• License: http://creativecommons.org/licenses/by/4.0/
• 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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