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Studies of functional MRI data are increasingly concerned with the estimationof differences in spatio-temporal networks across groups of subjects orexperimental conditions. Unsupervised clustering and independent componentanalysis (ICA) have been used to identify such spatio-temporal networks. Whilethese approaches have been useful for estimating these networks at thesubject-level, comparisons over groups or experimental conditions requirefurther methodological development. In this paper, we tackle this problem byshowing how self-organizing maps (SOMs) can be compared within a Frecheaninferential framework. Here, we summarize the mean SOM in each group as aFrechet mean with respect to a metric on the space of SOMs. We consider the useof different metrics, and introduce two extensions of the classical sum ofminimum distance (SMD) between two SOMs, which take into account thespatio-temporal pattern of the fMRI data. The validity of these methods isillustrated on synthetic data. Through these simulations, we show that thethree metrics of interest behave as expected, in the sense that the onescapturing temporal, spatial and spatio-temporal aspects of the SOMs are morelikely to reach significance under simulated scenarios characterized bytemporal, spatial and spatio-temporal differences, respectively. In addition, are-analysis of a classical experiment on visually-triggered emotionsdemonstrates the usefulness of this methodology. In this study, themultivariate functional patterns typical of the subjects exposed to pleasantand unpleasant stimuli are found to be more similar than the ones of thesubjects exposed to emotionally neutral stimuli. Taken together, these resultsindicate that our proposed methods can cast new light on existing data byadopting a global analytical perspective on functional MRI paradigms.

Group Analysis of Self-organizing Maps based on Functional MRI using Restricted Frechet Means