论文标题
在无与伦比的空间上对齐时间序列
Aligning Time Series on Incomparable Spaces
论文作者
论文摘要
动态时间扭曲（DTW）是对齐，比较和组合时间序列的有用方法，但它要求它们生活在可比的空间中。在这项工作中，我们考虑了一个设置，即时间序列在不同的空间上无明智的地面度量，从而导致DTW变得不确定。为了减轻这一点，我们提出了Gromov动态时间扭曲（GDTW），这是在潜在无与伦比的空间上的时间序列之间的距离，该距离避免了相关的几何形状，从而避免了可比性要求。我们证明了它在对齐，结合和比较生活在无与伦比的空间上的时间序列方面的有效性。我们进一步建议将GDTW的平滑版本作为可区分的损失，并在各种环境中评估其特性，包括Barycentric平均，生成的建模和模仿学习。
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.
