This paper considers analysis of human brain networks or graphs constructed from time-series collected from functional magnetic resonance imaging (fMRI). In the network of time-series, the nodes describe the regions and the edge weights correspond to the absolute values of correlation coefficients of the time-series of the two nodes associated with the edges. The paper introduces a novel information-theoretic metric, referred as sub-graph entropy, to measure uncertainty associated with a sub-graph. Nodes and edges constitute two special cases of sub-graph structures. Node and edge entropies are used in this paper to rank regions and edges in a functional brain network. The paper analyzes task-fMRI data collected from 475 subjects in the Human Connectome Project (HCP) study for gambling and emotion tasks. The proposed approach is used to rank regions and edges associated with these tasks. The differential node (edge) entropy metric is defined as the difference of the node (edge) entropy corresponding to two different networks belonging to two different classes. Differential entropy of nodes and edges are used to rank top regions and edges associated with the two classes of data. Using top node and edge entropy features separately, two-class classifiers are designed using support vector machine (SVM) with radial basis function (RBF) kernel and leave-one-out method to classify time-series for emotion task vs. no-task, gambling task vs. no-task and emotion task vs. gambling task. Using node entropies, the SVM classifier achieves classification accuracies of 0.96, 0.97 and 0.98, respectively. Using edge entropies, the classifier achieves classification accuracies of 0.91, 0.96 and 0.94, respectively.
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