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.