Network classification with applications to brain connectomics
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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 (or graph) classification problem. Existing approaches to graph classification tend to either treat all edge weights as a long vector, ignoring the network structure, or focus on the graph topology while ignoring the edge weights. Our goal here is to design a graph classification method that uses both the individual edge information and the network structure of the data in a computationally efficient way. We are also interested in obtaining a parsimonious and interpretable representation of differences in brain connectivity patterns between classes, which requires variable selection. We propose a graph classification method that uses edge weights as variables but incorporates the network nature of the data via penalties that promotes sparsity in the number of nodes. We implement the method via efficient convex optimization algorithms and show good performance on data from two fMRI studies of schizophrenia.
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