Discriminative log-euclidean kernels for learning on brain networks

Abstract

The increasing availability of functional Magnetic Resonance Imaging (fMRI) has led to a number of studies of brain networks with the aim of developing computer aided diagnosis of disease. Typically these are based on a statistical or machine learning method operating on connectivity networks, or features derived from them. This work presents a novel kernel method allowing classification tasks on connectivity networks represented as symmetric positive definite (SPD) matrices. It defines a kernel based on geodesic distances measured on the Riemannian manifold of SPD matrices, and automatically adjusts the eigenvalues of the matrices to improve accuracy. This is coupled with a Gaussian Process (GP) classifier, and used to discriminate healthy controls from Schizophrenia patients. The new kernel offers superior classification accuracy to previous kernels, and the adjusted eigenvalues allow discovery of clinically meaningful differences in connectivity between patients and controls.