Time Series Classification with Elasticity Using Augmented Path Signatures

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We often compare time-dependent data elastically such that some compression or dilation along the time dimension can be ignored, for example, spatial trajectories of vehicles moving at different speeds or accelerometer data for exercises completed at variable rhythms. Traditionally this is possible via an alignment-based elastic distance measure, such as Dynamic Time Warping (DTW). We may also control the degree of allowable warping with warping constraints. However, these elastic distance measures are not easy to use in large scale time series classification, as they need to be evaluated pairwise and often cannot be directly converted into feature sets that we may use with arbitrary classifiers or combine with other features. In this research, we focus on the study of path signatures, a transformation with time warping invariance property, and how we may augment a time series to make its signature space representation reflect common warping constraints. We demonstrate that the comparing signatures is analogous to comparing time series with elastic distances, and that augmented signature features can serve as warping invariant or insensitive features in time series classification. Finally, we construct Multiple Path Signatures with Constraining Augmentations Classifier (MultiPSCA), a general-purpose minimal tuning time series classifier using augmented signatures, and show that it is able to beat existing best-performing elastic time series classification algorithms without per-dataset hyperparameter tuning.