A Generalised Signature Method for Multivariate Time Series Feature Extraction

Abstract

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 generalised signature method that contains these variations as special cases, and groups them conceptually into augmentations, windows, transforms, and 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. * Equal contribution Preprint. Under review.

The FreshPRINCE: A Simple Transformation Based Pipeline Time Series Classifier

“…Generalised Signatures [23] are a set of feature extraction techniques primarily for multivariate time series based on rough path theory. We specifically look at the generalised signature method [23] and the accompanying canonical signature pipeline. Signatures are collections of ordered cross-moments.…”

Conditional Sig-Wasserstein GANs for Time Series Generation

“…In our work, we use three augumentation methods (a) Time augumentation, (b) Visiability transformation, and (c) Lead-lag transformation, which add the extra feature dimension to encode the information on the time stamps, the starting point of the path and the lagged process respectively. We refer [14] for the precise definition of the above path augmentations. For ease of notation, we denote the space of the time-augmented and visibility transformed paths of finite p-variation by Ω p 0 (J, E).…”

Functional linear regression with truncated signatures

“…For any path X ∈ BV (R d ), we will consider the time-augmented path (X t , t) ∈ BV (R d+1 ), which satisfies the assumption of Proposition 2.3. Enriching the path with new dimensions is a classic part of the learning process when signatures are used, and is discussed by Fermanian (2019) and Morrill et al (2020).…”