The human brain comprises an intricate web of connections that generate complex neural networks capable of storing and processing information based on factors such as network structure, connectivity strength, and interactions. To further unravel and understand this information, we introduce third-order entropy, a new metric grounded in the Triple Correlation Uniqueness (TCU) theorem. Triple correlation, which provides a complete and unique characterization of the network, relates three nodes separated by up to two spatiotemporal lags. Based on these four lags, we evaluate third-order entropy from the spatiotemporal lag probability distribution function (PDF) of the network activity's triple correlation. Given a spike raster, we compute triple correlation by iterating over time and space. Summing the contributions to the triple correlation over each of the spatial and temporal lag combinations generates a 4-D spatiotemporal frequency histogram, from which we estimate a PDF and compute entropy. To validate our approach, we first estimate third-order entropy from feedforward motifs in a simulated spike raster and then simulate the effects of adding increasing motif-class structure to a Poisson-modeled spike raster. Finally, we apply this methodology to spiking activity recorded from rat cortical cultures and compare our results to previously published results of pairwise entropy over time. Although first- and second-order metrics of activity (spike rate and cross-correlation) show agreement with previously published results, our TCU-based third-order entropy computation is a more complete tool for neural network characterization and reveals a greater depth of underlying network organization compared with pairwise entropy.NEW & NOTEWORTHY Here, we present third-order entropy built from triple correlation, which measures spatiotemporal interactions among up to three neurons. Per the Triple Correlation Uniqueness theorem, third-order entropy is based on a complete and unique characterization of the network. We first outline and validate the method and then apply it to an experimental dataset of rat cortical cultures. We show that the third-order entropy metric provides greater insight into network activity compared with pairwise entropy.
Keywords: Triple Correlation Uniqueness theorem; entropy; neural network characterization.