CDPS: Constrained DTW-Preserving Shapelets

Abstract

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. The presence of phase shift, differences in sample duration, and/or compression and dilation of a signal means that Euclidean distance is unsuitable in many cases. 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 Learning DTW-Preserving Shapelets (LDPS) have been developed to regain these properties by using the concept of shapelet transform. LDPS learns an unsupervised representation that models DTW distances using Euclidean distance in shapelet space. 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 fulfils 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. CLDPS is shown to outperform the state-of-the-art constrained-clustering algorithms on multiple time-series datasets. An open-source implementation based on PyTorch is available From: https://git.unistra.fr/helamouri/constrained-dtw-preserving-shapelets, which takes full advantage of GPU acceleration.