In this paper we construct an atlas that summarizes functional connectivity characteristics of a cognitive process from a population of individuals. The atlas encodes functional connectivity structure in a low-dimensional embedding space that is derived from a diffusion process on a graph that represents correlations of fMRI time courses. The functional atlas is decoupled from the anatomical space, and thus can represent functional networks with variable spatial distribution in a population. In practice the atlas is represented by a common prior distribution for the embedded fMRI signals of all subjects. We derive an algorithm for fitting this generative model to the observed data in a population. Our results in a language fMRI study demonstrate that the method identifies coherent and functionally equivalent regions across subjects. The method also successfully maps functional networks from a healthy population used as a training set to individuals whose language networks are affected by tumors.National Science Foundation (U.S.). Division of Information & Intelligent Systems (Collaborative Research in Computational Neuroscience Grant 0904625)National Science Foundation (U.S.) (CAREER Grant 0642971)National Institutes of Health (U.S.) (National Center for Research Resources (U.S.)/Neuroimaging Analysis Center (U.S.) P41-RR13218)National Institutes of Health (U.S.) (National Institute for Biomedical Imaging and Bioengineering (U.S.)/Neuroimaging Analysis Center (U.S.) P41-EB-015902)National Institutes of Health (U.S.) (National Institute for Biomedical Imaging and Bioengineering (U.S.)/National Alliance for Medical Image Computing (U.S.) U54-EB005149)National Institutes of Health (U.S.) (U41RR019703)National Institutes of Health (U.S.) (Eunice Kennedy Shriver National Institute of Child Health and Human Development (U.S.) R01HD067312)National Institutes of Health (U.S.) (P01CA067165)Brain Science FoundationKlarman Family FoundationEuropean Commission (FP7/2007–2013) n°257528 (KHRESMOI))European Commission (330003 (FABRIC))Austrian Science Fund (P 22578-B19 (PULMARCH)
