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.

Information parity increases on functional brain networks under influence of a psychedelic substance

“…This suggests that regardless of the individual configuration that brain adopts under the psychedelic influence, it will choose a configuration that increases information parity on the functional networks. Previous works have pointed to an increase of flexibility in functional brain networks under Ayahuasca influence, which has been measured by an increase in entropy of the correlation map [15], the increase of diversity of influences [13], and the increase on entropy of connectivity distribution [3]. The present results lead us to hypothesize that the rise in entropy may be coordinated with an increase in redundancy, when pairs of nodes tend to gather more homologous information.…”

“…However, one should consider the limitation of the data: (i) the number of individuals are small, which does not allow us to rely on traditional statistical tests well established in the field of neuroscience; (ii) our experimental design did not include a placebo group; (iii) for the local analysis, we choose the clusters of regions based on neuroscience literature instead perform a systematic network's modular inspection; (iv) to avoid misleading conclusions given the limited size of the data, we did not perform a detailed analysis for each brain region. Hence, in order have a more conclusive picture of changes on the brain functions in non ordinary state of consciousness, we recommend a replication of the analysis performed here, alongside to the previous analysis [3,13,15], for a large group of individuals. It invites investigations for other altered states of consciousness as well.…”

“…Recent studies have shown that under psychedelic influence the brain functions become less constrained as indicated by increasing entropy in different aspects of brain activity [1,3,13,15,31]. Along the increase on entropy, previous results have indicated an increase in network segregation after Ayahuasca intake characterized by an increase of local efficiency, clustering coefficient, and geodesic distances and a decrease of global efficiency [3].…”

Atomic Lattice Resolved Electron Tomography of a 3D Self‐Assembled Mesocrystal

“…A more direct measure of orientation distribution is orientation entropy, which quantifies the randomness of the orientation distribution in 3D space for each layer (Section S8, Supporting Information). [ 48–50 ] Figure 4d shows that the orientational entropy and θ ij follow the same trend. Both the average NN misalignment and the distribution of NN misalignments increase from C1 to C5 and decrease from C5 to C9.…”

Information Theory Inspired Pattern Analysis for Time-series Data

“…One of the key points to calculate VN is to obtain the density operator ρ, which must satisfy (i) be Hermitian, (ii) have unit trace, and (iii) be positive semidefinite. Given R ∈ R N , an N-dimension Pearson correlation matrix of the human activity data, then the density operator ρ can be defined as [47]:…”