Grassmann manifold learning for discriminant analysis of functional connectivity patterns
The functional brain networks, extracted from fMRI images using independent component analysis, have been demonstrated informative for distinguishing brain states of cognitive function and brain disorders. We develop a manifold learning technique for discriminant analysis of functional brain networks jointly at an individual level, rather than analyzing each network encoded by a spatial independent component separately. The functional brain networks of each individual are used as bases for a linear subspace, referred to as a functional connectivity pattern, which facilitates a comprehensive characterization of fMRI data. The functional connectivity patterns of different individuals are analyzed on the Grassmann manifold by adopting a principal angle based Riemannian distance. In conjunction with a support vector machine classifier, a forward component selection technique is proposed to select independent components for constructing the most discriminative functional connectivity pattern. The discriminant analysis method has been applied to fMRI based studies of schizophrenia, Alzheimer’s disease, Wilson's disease, and smokers.
 Fan, Y., et al., Discriminant analysis of functional connectivity patterns on Grassmann manifold, Neuroimage, 2011. 56(4):2058–2067