Threshold-free estimation of entropy from a Pearson matrix
Helcio Felippe, Aline Viol, Dráulio Barros de Araújo, M. G. E. da Luz, Fernanda Palhano-Fontes, Heloisa Onias, Ernesto P. Raposo, G. M. Viswanathan
Europhysics Letters January 24, 2023 DOI: 10.1209/0295-5075/acb5bd (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Methodological paper with demonstration Peer reviewed |
|---|---|
| Keywords | Thresholding Entropy estimation Statistics Artificial intelligence Pattern recognition psychology Applied mathematics Estimator |
| Citations | 9 |
| Key points | A unique entropy can be estimated directly from a Pearson correlation matrix without thresholding. |
Abstract
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.