  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.
