Time Series Classification through Diffeomorphic Time Warping (DiffTW)

The article introduces Diffeomorphic Time Warping (DiffTW), a theoretical framework for time series classification that learns mappings between real-valued functions to overcome the discrete point matching limitations of Dynamic Time Warping (DTW). DiffTW approximates diffeomorphic transformations using the method of characteristics to solve linear transport equations, providing a theoretically grounded dissimilarity measure.

• The method models system dynamics via ordinary differential equations derived from the fundamental theorem of calculus.
• Flexible velocity field representations are enabled using reproducing kernel Hilbert spaces and optimal control methods.
• Evaluation using a 1-nearest neighbor classifier shows DiffTW outperforms DTW on 60 of 86 datasets.