A graph theoretical regression model for brain connectivity learning of Alzheimer´S disease

Learning functional brain connectivity is essential to the understanding of neurodegenerative diseases. In this paper, we introduce a novel graph regression model (GRM) which regards the imaging data as signals defined on a graph and optimizes the fitness between the graph and the data, with a sparsity level regularization. The proposed framework features a nice interpretation in terms of low-pass signals on graphs, and is more generic compared with the previous statistical models. Results based on the simulated data illustrates that our approach can obtain a very close reconstruction of the true network. We then apply the GRM to learn the brain connectivity of Alzheimer´s disease (AD). Evaluations performed upon PET imaging data of 30 AD patients demonstrate that the connectivity patterns discovered are easy to interpret and consistent with known pathology.