Generalised Interpretable Shapelets for Irregular Time Series

TL;DR

This paper extends the shapelet transform to handle irregularly-sampled, partially-observed multivariate time series in continuous time, improving interpretability and efficiency while enabling shapelet length learning and a learned similarity measure.

Contribution

It introduces a continuous-time, interpretable shapelet transform for irregular time series with differentiable shapelet length learning and a learned pseudometric for similarity.

Findings

Successfully applied to multiple datasets demonstrating interpretability.

Discovered meaningful features such as digit chirality and spectral gaps.

Enhanced performance over previous shapelet methods.

Abstract

The shapelet transform is a form of feature extraction for time series, in which a time series is described by its similarity to each of a collection of `shapelets'. However it has previously suffered from a number of limitations, such as being limited to regularly-spaced fully-observed time series, and having to choose between efficient training and interpretability. Here, we extend the method to continuous time, and in doing so handle the general case of irregularly-sampled partially-observed multivariate time series. Furthermore, we show that a simple regularisation penalty may be used to train efficiently without sacrificing interpretability. The continuous-time formulation additionally allows for learning the length of each shapelet (previously a discrete object) in a differentiable manner. Finally, we demonstrate that the measure of similarity between time series may be generalised to a learnt pseudometric. We validate our method by demonstrating its performance and interpretability on several datasets; for example we discover (purely from data) that the digits 5 and 6 may be distinguished by the chirality of their bottom loop, and that a kind of spectral gap exists in spoken audio classification.