Invariants of multidimensional time series based on their iterated-integral signature

TL;DR

This paper presents a new set of features derived from Chen's iterated-integral signature that are invariant under various transformations such as linear, rotational, and permutation groups for multidimensional time series.

Contribution

The authors develop a novel class of invariant features for multidimensional time series based on the iterated-integral signature, extending the applicability of these features under different transformations.

Findings

Features are invariant under linear transformations.

Features are invariant under rotations.

Features are invariant under axis permutations.

Abstract

We introduce a novel class of features for multidimensional time series, that are invariant with respect to transformations of the ambient space. The general linear group, the group of rotations and the group of permutations of the axes are considered. The starting point for their construction is Chen's iterated-integral signature.