Aligning Time Series on Incomparable Spaces
arXiv:2006.12648
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.
References in corpus (9)
- Learning Continuous Control Policies by Stochastic Value Gradients
- Faster Retrieval with a Two-Pass Dynamic-Time-Warping Lower Bound
- Optimal Transport for structured data with application on graphs
- Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
- Convergence Rate of Frank-Wolfe for Non-Convex Objectives
- Gromov-Wasserstein Learning for Graph Matching and Node Embedding
- Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching
- Partial Optimal Transport with Applications on Positive-Unlabeled Learning
- Time Series Alignment with Global Invariances