Quantum Edge Entropy for Alzheimer's Disease Analysis

摘要

In this paper, we explore how to the decompose the global statistical mechanical entropy of a network into components associated with its edges. Commencing from a statistical mechanical picture in which the normalised Laplacian matrix plays the role of Hamiltonian operator, thermodynamic entropy can be calculated from partition function associated with different energy level occupation distributions arising from Bose-Einstein statistics and Fermi-Dirac statistics. Using the spectral decomposition of the Laplacian, we show how to project the edge-entropy components so that the detailed distribution of entropy across the edges of a network can be achieved. We apply the resulting method to fMRI activation networks to evaluate the qualitative and quantitative characterisations. The entropic measurement turns out to be an effective tool to identify the differences in structure of Alzheimer's disease by selecting the most salient anatomical brain regions.