While the prevalence of Autism Spectrum Disorder (ASD) is increasing, research continues in an effort to identify common etiological and pathophysiological bases. In this regard, modern machine learning and network science pave the way for a better understanding of the neuropathology and the development of diagnosis aid systems. The present work addresses the classification of neurotypical and ASD subjects by combining knowledge about both the structure and the functional activity of the brain. In particular, we model the brain structure as a graph, and the resting-state functional MRI (rs-fMRI) signals as values that live on the nodes of that graph. We then borrow tools from the emerging field of Graph Signal Processing (GSP) to build features related to the frequency content of these signals. In order to make these features highly discriminative, we apply an extension of the Fukunaga-Koontz transform. Finally, we use these new markers to train a decision tree, an interpretable classification scheme, which results in a final diagnosis aid model. Interestingly, the resulting decision tree outperforms state-of-the-art methods on the publicly available Autism Brain Imaging Data Exchange (ABIDE) collection. Moreover, the analysis of the predictive markers reveals the influence of the frontal and temporal lobes in the diagnosis of the disorder, which is in line with previous findings in the literature of neuroscience. Our results indicate that exploiting jointly structural and functional information of the brain can reveal important information about the complexity of the neuropathology.

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