fMRI Activation Network Analysis Using Bose-Einstein Entropy

In this paper, we present a novel method for characterizing networks using the entropy associated with bosonic particles in thermal equilibrium with a heat-bath. According to this analogy, the normalized Laplacian plays the role of Hamiltonian operator, and the associated energy states are populated according to Bose-Einstein statistics. This model is subject to thermal agitation by the heat reservoir. The physics of the system can be captured by using a partition function defined over the normalized Laplacian eigenvalues. Various global thermodynamic characterizations of the network including its entropy and energy then can be computed from the derivative of corresponding partition function with respect to temperature. We explore whether the resulting entropy can be used to construct an effective information theoretic graph-kernel for the purposes of classifying different types of graph or network structure. To this end, we construct a Jensen-Shannon kernel using the Bose-Einstein entropy for a sample of networks, and then apply kernel principle components analysis (kPCA) to map graphs into low dimensional feature space. We apply the resulting method to classify fMRI activation networks from patients with suspected Alzheimer disease.