Connectivity matrices obtained from various modalities (DTI, MEG and fMRI) provide a unique insight into brain processes. Their high dimensionality necessitates the development of methods for population-based statistics, in the face of small sample sizes. In this paper, we present such a method applicable to functional connectivity networks, based on identifying the basis of dominant connectivity components that characterize the patterns of brain pathology and population variation. Projection of individual connectivity matrices into this basis allows for dimensionality reduction, facilitating subsequent statistical analysis. We find dominant components for a collection of connectivity matrices by using the projective non-negative component analysis technique which ensures that the components have non-negative elements and are non-negatively combined to obtain individual subject networks, facilitating interpretation. We demonstrate the feasibility of our novel framework by applying it to simulated connectivity matrices as well as to a clinical study using connectivity matrices derived from resting state magnetoencephalography (MEG) data in a population of subjects diagnosed with autism spectrum disorder (ASD).