  We propose a novel optimization framework to predict clinical severity from
resting state fMRI (rs-fMRI) data. Our model consists of two coupled terms. The
first term decomposes the correlation matrices into a sparse set of
representative subnetworks that define a network manifold. These subnetworks
are modeled as rank-one outer-products which correspond to the elemental
patterns of co-activation across the brain; the subnetworks are combined via
patient-specific non-negative coefficients. The second term is a linear
regression model that uses the patient-specific coefficients to predict a
measure of clinical severity. We validate our framework on two separate
datasets in a ten fold cross validation setting. The first is a cohort of
fifty-eight patients diagnosed with Autism Spectrum Disorder (ASD). The second
dataset consists of sixty three patients from a publicly available ASD
database. Our method outperforms standard semi-supervised frameworks, which
employ conventional graph theoretic and statistical representation learning
techniques to relate the rs-fMRI correlations to behavior. In contrast, our
joint network optimization framework exploits the structure of the rs-fMRI
correlation matrices to simultaneously capture group level effects and patient
heterogeneity. Finally, we demonstrate that our proposed framework robustly
identifies clinically relevant networks characteristic of ASD.
