Correlation Analysis With Scale-local Entropy Measures

TL;DR

This paper introduces a new correlation analysis method based on scale-dependent Renyi entropies, providing explicit entropy functions and demonstrating its effectiveness on various point-set data.

Contribution

It presents a novel scale-local entropy approach for correlation analysis, including analytic derivations and validation against Monte Carlo simulations.

Findings

Derived explicit formulas for dithered scale-local entropy and dimension.

Validated the method with Monte Carlo simulations and nontrivial point-set correlations.

Showed the method's ability to analyze condensation and clustering phenomena.

Abstract

A novel method for correlation analysis using scale-dependent Renyi entropies is described. The method involves calculating the entropy of a data distribution as an explicit function of the scale of a d-dimensional partition of d-cubes, which is dithered to remove bias. Analytic expressions for dithered scale-local entropy and dimension for a uniform random point set are derived and compared to Monte Carlo results. Simulated nontrivial point-set correlations representing condensation and clustering are similarly analyzed.