Measuring dependencies between variables of a dynamical system using fuzzy affiliations

TL;DR

The paper introduces a data-driven approach using fuzzy affiliations and linear mappings to quantify influences between variables in dynamical systems, demonstrated through theoretical analysis and real-world examples.

Contribution

It presents a novel method combining fuzzy affiliations and linear mappings to measure variable dependencies in dynamical systems.

Findings

Method effectively quantifies influences between variables.

The approach is validated with theoretical analysis.

Numerical examples include real-world basketball data.

Abstract

A statistical, data-driven method is presented that quantifies influences between variables of a dynamical system. The method is based on finding a suitable representation of points by fuzzy affiliations with respect to landmark points using the Scalable Probabilistic Approximation algorithm. This is followed by the construction of a linear mapping between these affiliations for different variables and forward in time. This linear mapping can be directly interpreted in light of unidirectional dependencies and relevant properties of it are quantified. These quantifications then serve as measures for the influences between variables of the dynamics. The validity of the method is demonstrated with theoretical results and on several numerical examples, including real-world basketball player movement.