Hypergraphs on high dimensional time series sets using signature transform

TL;DR

This paper introduces a novel method for constructing hypergraphs from collections of high-dimensional time series using signature transforms, improving robustness and applicability over previous single-series approaches.

Contribution

It extends existing hypergraph construction methods to collections of multivariate time series by leveraging signature transforms for enhanced robustness.

Findings

Validated on synthetic datasets with promising results

Generalizes previous single-series methods to collections

Uses signature transforms to improve construction robustness

Abstract

In recent decades, hypergraphs and their analysis through Topological Data Analysis (TDA) have emerged as powerful tools for understanding complex data structures. Various methods have been developed to construct hypergraphs -- referred to as simplicial complexes in the TDA framework -- over datasets, enabling the formation of edges between more than two vertices. This paper addresses the challenge of constructing hypergraphs from collections of multivariate time series. While prior work has focused on the case of a single multivariate time series, we extend this framework to handle collections of such time series. Our approach generalizes the method proposed in Chretien and al. by leveraging the properties of signature transforms to introduce controlled randomness, thereby enhancing the robustness of the construction process. We validate our method on synthetic datasets and present promising results.