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Kernel partial least squares regression for relating functional brain network topology to clinical measures of behavior

In this paper we present a novel method for analyzing the relationship between functional brain networks and behavioral phenotypes. Drawing from topological data analysis, we first extract topological features using persistent homology from functional brain networks that are derived from correlations in resting-state fMRI. Rather than fixing a discrete network topology by thresholding the connectivity matrix, these topological features capture the network organization across all continuous threshold values. We then propose to use a kernel partial least squares (kPLS) regression to statistically quantify the relationship between these topological features and behavior measures. The kPLS also provides an elegant way to combine multiple image features by using linear combinations of multiple kernels. In our experiments we test the ability of our proposed brain network analysis to predict autism severity from rs-fMRI. We show that combining correlations with topological features gives better prediction of autism severity than using correlations alone.