Threshold-free estimation of entropy from a Pearson matrix

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.

arXiv comment12 pages, 6 figures

References in corpus (15)

• Statistical mechanics of complex networks
• Efficient Behavior of Small-World Networks
• Scale-free brain functional networks
• Weight-conserving characterization of complex functional brain networks
• Layer aggregation and reducibility of multilayer interconnected networks
• Enhanced repertoire of brain dynamical states during the psychedelic experience
• A small-world of weak ties provides optimal global integration of self-similar modules in functional brain networks
• Entropy measures for complex networks: Toward an information theory of complex topologies
• Entropy Rate of Diffusion Processes on Complex Networks
• Correlation, Network and Multifractal Analysis of Global Financial Indices
• Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca
• Weight Thresholding on Complex Networks
• Characterizing complex networks using Entropy-degree diagrams: unveiling changes in functional brain connectivity induced by Ayahuasca
• Thresholding normally distributed data creates complex networks
• Enhancing transport properties in interconnected systems without altering their structure