Threshold-free estimation of entropy from a Pearson matrix

TL;DR

This paper introduces a threshold-free method to estimate the entropy of correlation matrices directly from Pearson matrices, avoiding arbitrary thresholding and applicable to neuroimaging data.

Contribution

It proposes an objective, general approach to compute a unique entropy from Pearson matrices, extending von Neumann entropy concepts without thresholding.

Findings

Successfully estimated brain entropy under psychedelic influence

Method avoids arbitrary thresholding in correlation-based entropy estimation

Applicable to diverse fields requiring correlation entropy measurement

Abstract

There is demand in diverse fields for a reliable method of estimating the entropy associated with correlations. The estimation of a unique entropy directly from the Pearson correlation matrix has remained an open problem for more than half a century. All existing approaches lack generality insofar as they require thresholding choices that arbitrarily remove possibly important information. Here we propose an objective procedure for directly estimating a unique entropy of a general Pearson matrix. We show that upon rescaling the Pearson matrix satisfies all necessary conditions for an analog of the von Neumann entropy to be well defined. No thresholding is required. We demonstrate the method by estimating the entropy from neuroimaging time series of the human brain under the influence of a psychedelic.