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

TL;DR

This paper introduces a novel framework for comparing self-organizing maps derived from fMRI data across groups using Frechet means and specialized metrics, enabling more effective group-level analysis of spatio-temporal brain networks.

Contribution

It develops a Frechet mean-based approach for comparing SOMs in fMRI studies, incorporating new metrics that account for spatio-temporal patterns, validated through simulations and real data.

Findings

Metrics effectively distinguish temporal, spatial, and spatio-temporal differences.

Method successfully re-analyzes fMRI data, revealing meaningful group differences.

Proposed approach enhances group comparison in functional MRI analysis.

Abstract

Studies of functional MRI data are increasingly concerned with the estimation of differences in spatio-temporal networks across groups of subjects or experimental conditions. Unsupervised clustering and independent component analysis (ICA) have been used to identify such spatio-temporal networks. While these approaches have been useful for estimating these networks at the subject-level, comparisons over groups or experimental conditions require further methodological development. In this paper, we tackle this problem by showing how self-organizing maps (SOMs) can be compared within a Frechean inferential framework. Here, we summarize the mean SOM in each group as a Frechet mean with respect to a metric on the space of SOMs. We consider the use of different metrics, and introduce two extensions of the classical sum of minimum distance (SMD) between two SOMs, which take into account the spatio-temporal pattern of the fMRI data. The validity of these methods is illustrated on synthetic data. Through these simulations, we show that the three metrics of interest behave as expected, in the sense that the ones capturing temporal, spatial and spatio-temporal aspects of the SOMs are more likely to reach significance under simulated scenarios characterized by temporal, spatial and spatio-temporal differences, respectively. In addition, a re-analysis of a classical experiment on visually-triggered emotions demonstrates the usefulness of this methodology. In this study, the multivariate functional patterns typical of the subjects exposed to pleasant and unpleasant stimuli are found to be more similar than the ones of the subjects exposed to emotionally neutral stimuli. Taken together, these results indicate that our proposed methods can cast new light on existing data by adopting a global analytical perspective on functional MRI paradigms.