  Predicting clinical variables from whole-brain neuroimages is a high
dimensional problem that requires some type of feature selection or extraction.
Penalized regression is a popular embedded feature selection method for high
dimensional data. For neuroimaging applications, spatial regularization using
the $\ell_1$ or $\ell_2$ norm of the image gradient has shown good performance,
yielding smooth solutions in spatially contiguous brain regions. However,
recently enormous resources have been devoted to establishing structural and
functional brain connectivity networks that can be used to define spatially
distributed yet related groups of voxels. We propose using the fused sparse
group lasso penalty to encourage structured, sparse, interpretable solutions by
incorporating prior information about spatial and group structure among voxels.
We present optimization steps for fused sparse group lasso penalized regression
using the alternating direction method of multipliers algorithm. With
simulation studies and in application to real fMRI data from the Autism Brain
Imaging Data Exchange, we demonstrate conditions under which fusion and group
penalty terms together outperform either of them alone. Supplementary materials
for this article are available online.
