A review of univariate and multivariate multifractal analysis illustrated by the analysis of marathon runners physiological data

TL;DR

This paper reviews wavelet-based multifractal analysis methods, extending them to multivariate cases, and demonstrates their application on physiological data from marathon runners to analyze joint signal singularities.

Contribution

It introduces the extension of wavelet multifractal analysis to multivariate signals and discusses the underlying mathematical questions.

Findings

Wavelet methods effectively analyze pointwise singularities.

Multivariate analysis captures joint singularities of multiple signals.

Application to marathon data reveals complex physiological signal interactions.

Abstract

We review the central results concerning wavelet methods in multifractal analysis, which consists in analysis of the pointwise singularities of a signal, and we describe its recent extension to multivariate multifractal analysis, which deals with the joint analysis of several signals; we focus on the mathematical questions that this new techniques motivate. We illustrate these methods by an application to data recorded on marathon runners.