Functional Magnetic Resonance Imaging (fMRI) is widely adopted to measure brain activity, aiming at studying brain functions both in healthy and pathological subjects. Discrimination and identification of functional alterations in the connectivity, characterizing mental disorders, are getting increasing attention in neuroscience community. We present a kernel-based method allowing to classify functional networks and characterizing those features that are significantly discriminative between two classes. We used a manifold approach based on Grassmannian geometry and graph Laplacians, which permits to learn a set of sub-connectivities that can be used in combination with Support Vector Machine (SVM) to classify functional connectomes and for identifying neuroanatomically different connections. We tested our approach on a real dataset of functional connectomes with subjects affected by Autism Spectrum Disorder (ASD), finding consistent results with the models of aberrant connections in ASD.