A Scaled-Correlation Based Approach for Defining and Analyzing Functional Networks

Abstract

Many natural systems can be described as networks of interacting elements, forming a graph of interactions. This is the case for climate models, coupled chemical systems, computer or social networks, or the brain. For many of these cases, dynamical networks emerge whose structure changes in time. Estimating the structure of such networks from the time series that describe the activity of their nodes is a serious challenge. Here, we devise a new method that is based on the Scaled Correlation function to estimate interactions between nodes that occur on fast timescales. We apply the method on EEG measurements from human volunteers to evaluate neuronal functional connectivity associated with a visual perception task. We compare the statistics of networks extracted with the new method with those that are extracted using traditional techniques, like the Pearson correlation coefficient or the cross-correlation function. Results indicate that the new method is superior in identifying networks whose structure correlates to the cognitive processes engaged during visual perception. The method is general enough to be applied on any data that describes dynamical interactions evolving on multiple timescales, as is the case in climate modeling, chemical networks, or complex biological systems.