CDPS: Constrained DTW-Preserving Shapelets

The analysis of time series for clustering and classification is becoming ever more popular because of the increasingly ubiquitous nature of IoT, satellite constellations, and handheld and smart-wearable devices, etc. Euclidean distance is unsuitable because of potential phase shift, differences in sample duration, and compression and dilation of characteristic signals. As such, several similarity measures specific to time-series have been proposed, Dynamic Time Warping (DTW) being the most popular. Nevertheless, DTW does not respect the axioms of a metric and therefore DTW-preserving shapelets have been developed to regain these properties. This unsupervised approach to representation learning models DTW properties through the shapelet transform. This article proposes constrained DTW-preserving shapelets (CDPS), in which a limited amount of user knowledge is available in the form of must link and cannot link constraints, to guide the representation such that it better captures the user’s interpretation of the data rather than the algorithm’s bias. Subsequently, any unconstrained algorithm can be applied, e.g. K-means clustering, k-NN classification, etc, to obtain a result that fulfills the constraints (without explicit knowledge of them). Furthermore, this representation is generalisable to out-of-sample data, overcoming the limitations of standard transductive constrained-clustering algorithms. The proposed algorithm is studied on multiple time-series datasets, and its advantages over classical constrained clustering algorithms and unsupervised DTW-preserving shapelets are demonstrated. An open-source implementation based on PyTorch is available to take full advantage of GPU acceleration