The analysis of fMRI data is challenging because they consist generally of a relatively modest signal contained in a high-dimensional space: a single scan can contain over 15 million voxel recordings over space and time. We present a method for classification and discrimination among fMRI that is based on modeling the scans as distance matrices, where each matrix measures the divergence of spatial network signals that fluctuate over time. We used single-subject independent components analysis (ICA), decomposing an fMRI scan into a set of statistically independent spatial networks, to extract spatial networks and time courses from each subject that have unique relationship with the other components within that subject. Mathematical properties of these relationships reveal information about the infrastructure of the brain by measuring the interaction between and strength of the components. Our technique is unique, in that it does not require spatial alignment of the scans across subjects. Instead, the classifications are made solely on the temporal activity taken by the subject's unique ICs. Multiple scans are not required and multivariate classification is implementable, and the algorithm is effectively blind to the subject-uniform underlying task paradigm. Classification accuracy of up to 90% was realized on a resting-scanned schizophrenia/normal dataset and a tasked multivariate Alzheimer's/old/young dataset. We propose that the ICs represent a plausible set of imaging basis functions consistent with network-driven theories of neural activity in which the observed signal is an aggregate of independent spatial networks having possibly dependent temporal activity.