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.

本文提出了一种基于 Gromov 得距离度量不可比较空间上的时间序列之间的距离的 Gromov dynamic time warping (GDTW) 方法，为解决传统 DTW 方法不能比较不同空间上的时间序列的问题提供了一种有效的解决方案，并通过实验在多个领域展示了 GDTW 的效能。