Exploring individual and group differences in latent brain networks using cross-validated simultaneous component analysis

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Component models such as PCA and ICA are often used to reduce neuroimaging data into a smaller number of components, which are thought to reflect latent brain networks. When data from multiple subjects are available, the components are typically estimated simultaneously (i.e., for all subjects combined) using either tensor ICA or group ICA. As we demonstrate in this paper, neither of these approaches is ideal if one hopes to find latent brain networks that cross-validate to new samples of data. Specifically, we note that the tensor ICA model is too rigid to capture real-world heterogeneity in the component time courses, whereas the group ICA approach is too flexible to uniquely identify latent brain networks. For multi-subject component analysis, we recommend comparing a hierarchy of simultaneous component analysis (SCA) models. Our proposed model hierarchy includes a flexible variant of the SCA framework (the Parafac2 model), which is able to both (i) model heterogeneity in the component time courses, and (ii) uniquely identify latent brain networks. Furthermore, we propose cross-validation methods to tune the relevant model parameters, which reduces the potential of over-fitting the observed data. Using simulated and real data examples, we demonstrate the benefits of the proposed approach for finding credible components that reveal interpretable individual and group differences in latent brain networks.