Cohen, S; Luise, G; Terenin, A; Amos, B; Deisenroth, MP; (2021) Aligning Time Series on Incomparable Spaces. In: Banerjee, A and Fukumizu, K, (eds.) Proceedings of the 24th International Conference on Artificial Intelligence and Statistics. (pp. pp. 1036-1044). PMLR

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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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