The `signature method' refers to a collection of feature extraction techniques for multimodal sequential data, derived from the theory of controlled differential equations. Variations exist as many authors have proposed modifications to the method, so as to improve some aspect of it. Here, we introduce a \emph{generalised signature method} that contains these variations as special cases, and groups them conceptually into \emph{augmentations}, \emph{windows}, \emph{transforms}, and \emph{rescalings}. Within this framework we are then able to propose novel variations, and demonstrate how previously distinct options may be combined. We go on to perform an extensive empirical study on 26 datasets as to which aspects of this framework typically produce the best results. Combining the top choices produces a canonical pipeline for the generalised signature method, which demonstrates state-of-the-art accuracy on benchmark problems in multivariate time series classification.

Signatory is a library for calculating signature and logsignature transforms and related functionality. The focus is on making this functionality available for use in machine learning, and as such includes features such as GPU support and backpropagation. To our knowledge it is the first publically available GPU-capable library for these operations. It also implements several new algorithmic improvements, and provides several new features not available in previous libraries. The library operates as a Python wrapper around C++, and is compatible with the PyTorch ecosystem. It may be installed directly via \texttt{pip}. Source code, documentation, examples, benchmarks and tests may be found at \texttt{\url{https://github.com/patrick-kidger/signatory}}. The license is Apache-2.0.