A Generalised Signature Method for Multivariate Time Series Feature Extraction
This work addresses the challenge of applying the signature method for time series analysis, making it more usable for machine learning practitioners, though it is incremental in unifying existing variations.
The paper unifies variations of the signature method for multivariate time series feature extraction into a generalised framework to make it more accessible to practitioners, and derives a canonical set of choices through an empirical study on 26 datasets, showing competitive performance in classification benchmarks.
The 'signature method' refers to a collection of feature extraction techniques for multivariate time series, derived from the theory of controlled differential equations. There is a great deal of flexibility as to how this method can be applied. On the one hand, this flexibility allows the method to be tailored to specific problems, but on the other hand, can make precise application challenging. This paper makes two contributions. First, the variations on the signature method are unified into a general approach, the \emph{generalised signature method}, of which previous variations are special cases. A primary aim of this unifying framework is to make the signature method more accessible to any machine learning practitioner, whereas it is now mostly used by specialists. Second, and within this framework, we derive a canonical collection of choices that provide a domain-agnostic starting point. We derive these choices as a result of an extensive empirical study on 26 datasets and go on to show competitive performance against current benchmarks for multivariate time series classification. Finally, to ease practical application, we make our techniques available as part of the open-source [redacted] project.