Soft-DTW Alignment Entropy
Soften a time-series alignment into weighted paths and separate expected cost from entropy.
Free theory articleSoften a time-series alignment into weighted paths and separate expected cost from entropy.
Concept & interpretation
Dynamic Time Warping (DTW) computes the optimal alignment between two time series by finding a path through a cost grid that minimizes the total cost. However, DTW is not smooth and its gradients are zero almost everywhere. Soft-DTW smooths this objective by replacing the hard minimum with a continuous log-sum-exp operator, taking into account all possible alignment paths.
Experiment
Observe how the Soft-DTW calculation shifts when changing the gamma smoothing factor in the Soft-DTW Alignment Entropy module:
- Set the series to "Identical" and smoothing gamma to 1. Note the Soft alignment cost is negative.
- Set the smoothing gamma to 0. Note that the Soft alignment cost equals the Hard DTW cost.