Spatio-Temporal Alignments: Optimal transport through space and time
This addresses the challenge of quantifying spatio-temporal variability for applications like pattern recognition and medical imaging, but it is incremental as it builds on existing DTW and OT methods.
The paper tackled the problem of comparing spatio-temporal data by proposing Spatio-Temporal Alignments (STA), a differentiable method combining Dynamic Time Warping and optimal transport to account for both temporal and spatial variability, with experiments on handwritten letters and brain imaging data showing its effectiveness.
Comparing data defined over space and time is notoriously hard, because it involves quantifying both spatial and temporal variability, while at the same time taking into account the chronological structure of data. Dynamic Time Warping (DTW) computes an optimal alignment between time series in agreement with the chronological order, but is inherently blind to spatial shifts. In this paper, we propose Spatio-Temporal Alignments (STA), a new differentiable formulation of DTW, in which spatial differences between time samples are accounted for using regularized optimal transport (OT). Our temporal alignments are handled through a smooth variant of DTW called soft-DTW, for which we prove a new property: soft-DTW increases quadratically with time shifts. The cost matrix within soft-DTW that we use are computed using unbalanced OT, to handle the case in which observations are not normalized probabilities. Experiments on handwritten letters and brain imaging data confirm our theoretical findings and illustrate the effectiveness of STA as a dissimilarity for spatio-temporal data.