A Canonical Signature-Based Feature Set for Multivariate Time Series Classification

Coming from the theory of controlled differential equations, the signature is a transformation used to extract features from multivariate time series. There is a great flexibility as to how this transformation can be applied. On the one hand, such flexibility allows the method to be tailored to specific problems, but on the other hand, it can make precise application challenging. This article makes two contributions. First, the variations of the signature method are unified into a general framework, the generalised signature method, of which previous variations are special cases. A primary goal of this unifying framework is to make the signature method more accessible to machine learning practitioners, whereas it is now mostly used by specialists. Second, and within this framework, we perform an extensive empirical study on 26 datasets to assess the relative performance of the different choices. As a result, we obtain a canonical feature set which provides a domain-agnostic starting point and shows competitive performance against current benchmarks for multivariate time series classification.