Selection entropy: the information hidden within neuronal patterns

Boltzmann entropy is a measure of the hidden information contained within a system. In the context of neuroimaging, information can be hidden within the multiple brain states that cannot be distinguished within a single image. Here, we show that information can also be hidden within multiple indistinguishable connections between neuronal regions, as quantified by a metric that we term ‘selection entropy’. We show the ways in which selection entropy behaves in comparison with the Kullback-Leibler (KL) divergence (relative entropy). Firstly, we use synthetic datasets to demonstrate that selection entropy is more sensitive to small changes in probability distributions as compared with the KL divergence. Secondly, we show that selection entropy identifies a principle gradient between sensorimotor and transmodal brain regions more definitively than the KL divergence within resting-state fMRI timeseries. As such, we introduce selection entropy as an additional asset in the analysis of neuronal functional selectivity.