A Generalised Signature Method for Multivariate Time Series Feature Extraction

Abstract

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.

arXiv comment25 pages

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Cited by in corpus (5)

• Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
• Neural Controlled Differential Equations for Online Prediction Tasks
• Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projections
• Efficient and Accurate Gradients for Neural SDEs
• Path Signature Area-Based Causal Discovery in Coupled Time Series