  While statistical analysis of a single network has received a lot of
attention in recent years, with a focus on social networks, analysis of a
sample of networks presents its own challenges which require a different set of
analytic tools. Here we study the problem of classification of networks with
labeled nodes, motivated by applications in neuroimaging. Brain networks are
constructed from imaging data to represent functional connectivity between
regions of the brain, and previous work has shown the potential of such
networks to distinguish between various brain disorders, giving rise to a
network classification problem. Existing approaches tend to either treat all
edge weights as a long vector, ignoring the network structure, or focus on
graph topology as represented by summary measures while ignoring the edge
weights. Our goal is to design a classification method that uses both the
individual edge information and the network structure of the data in a
computationally efficient way, and that can produce a parsimonious and
interpretable representation of differences in brain connectivity patterns
between classes. We propose a graph classification method that uses edge
weights as predictors but incorporates the network nature of the data via
penalties that promote sparsity in the number of nodes, in addition to the
usual sparsity penalties that encourage selection of edges. We implement the
method via efficient convex optimization and provide a detailed analysis of
data from two fMRI studies of schizophrenia.
