[Paper Review] Generalised Interpretable Shapelets for Irregular Time Series

Patrick Kidger, James Morrill+1 more|arXiv (Cornell University)|May 28, 2020

Time Series Analysis and Forecasting27 references6 citations

TL;DR

This paper introduces a continuous-time generalisation of the shapelet transform that enables end-to-end differentiable learning of interpretable, irregularly-sampled multivariate time series features. By formulating shapelets in continuous time and introducing a learnable pseudometric, the method achieves both high performance and interpretability—demonstrating discovery of structural patterns like chirality in digits and spectral gaps in audio.

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.

Motivation & Objective

• To overcome limitations of classical shapelet transforms, which are restricted to regularly-sampled, fully-observed time series.
• To enable differentiable training of shapelet length and position, removing the need for discrete hyperparameter search.
• To maintain interpretability while achieving efficient training through a simple regularisation penalty.
• To generalise the similarity measure between time series and shapelets to a learnable pseudometric for improved domain adaptation.
• To enable discovery of meaningful, data-driven patterns such as chirality in handwritten digits and spectral gaps in audio

Proposed method

• Formulates the shapelet transform in continuous time, allowing treatment of irregularly-sampled and partially-observed multivariate time series.
• Represents shapelets as continuous functions over time, enabling differentiable optimisation of their length and temporal position.
• Introduces a regularisation penalty that encourages shapelets to resemble salient, interpretable features in the data.
• Generalises the classical L2 discrepancy to a learnable pseudometric via a diagonal matrix A, allowing channel-specific weighting of similarity.
• Uses the MFC (Mel-frequency cepstral) representation of audio as input to the generalised shapelet transform for speech classification.
• Employs end-to-end backpropagation through the shapelet transform for joint optimisation of shapelets and downstream classifier

Experimental results

Research questions

• RQ1 Can shapelet learning be generalised to irregularly-sampled and partially-observed multivariate time series while preserving interpretability?
• RQ2 Can the length of shapelets be optimised differentiably rather than as a discrete hyperparameter?
• RQ3 Can a simple regularisation strategy maintain interpretability without sacrificing training efficiency?
• RQ4 Can a learnable pseudometric improve performance and provide insight into feature importance across channels?
• RQ5 Can the method discover novel, interpretable patterns in real-world time series data, such as chirality in digits or spectral gaps in audio?

Key findings

• The generalised shapelet transform achieved 91.9% ± 2.4% test accuracy on the Speech Commands dataset, significantly outperforming the classical shapelet transform (44.8% ± 8.6%).
• On the PenDigits dataset, the method achieved 93.5% ± 1.1% accuracy at 50% training data, demonstrating strong performance on small datasets.
• The model discovered that digits 5 and 6 can be distinguished by the chirality (direction) of their bottom loop, purely from data.
• In speech classification, the learned pseudometric identified a spectral gap, with higher weights assigned to the first 15 Mel-frequency cepstral coefficients, confirming the importance of low-frequency components.
• Shapelets learned in MFC space were perceptually interpretable—when converted back to audio, they resembled meaningful sounds like 'eft' or 'stop', indicating they capture discriminative features.
• The method achieved state-of-the-art performance on multiple benchmarks, including Libras and LSST, while maintaining interpretability through regularisation and visualisation