  Substantial evidence indicates that major psychiatric disorders are
associated with distributed neural dysconnectivity, leading to strong interest
in using neuroimaging methods to accurately predict disorder status. In this
work, we are specifically interested in a multivariate approach that uses
features derived from whole-brain resting state functional connectomes.
However, functional connectomes reside in a high dimensional space, which
complicates model interpretation and introduces numerous statistical and
computational challenges. Traditional feature selection techniques are used to
reduce data dimensionality, but are blind to the spatial structure of the
connectomes. We propose a regularization framework where the 6-D structure of
the functional connectome is explicitly taken into account via the fused Lasso
or the GraphNet regularizer. Our method only restricts the loss function to be
convex and margin-based, allowing non-differentiable loss functions such as the
hinge-loss to be used. Using the fused Lasso or GraphNet regularizer with the
hinge-loss leads to a structured sparse support vector machine (SVM) with
embedded feature selection. We introduce a novel efficient optimization
algorithm based on the augmented Lagrangian and the classical alternating
direction method, which can solve both fused Lasso and GraphNet regularized SVM
with very little modification. We also demonstrate that the inner subproblems
of the algorithm can be solved efficiently in analytic form by coupling the
variable splitting strategy with a data augmentation scheme. Experiments on
simulated data and resting state scans from a large schizophrenia dataset show
that our proposed approach can identify predictive regions that are spatially
contiguous in the 6-D "connectome space," offering an additional layer of
interpretability that could provide new insights about various disease
processes.
