Significance Estimation in fMRI from Random Matrices

Abstract

Indicative features of an fMRI data set can be evaluated by methods provided by theory of random matrices (RMT). RMT considers ensembles of matrices and yields statements on the properties of the typical eigensystems in these ensembles. The authors have studied the particular ensemble of random correlation matrices that can be used as a noise model for the empirical data and that allows us thus to select data features that significantly differ from the noisy background. In this sense RMT can be understood as offering a systematic approach to surrogate data. Interestingly, also the noise characteristics change between different experimental conditions. This is revealed by higher-order statistics available from RMT. The authors illustrate the RMT-based approach by an exemplary data set for the distinction between a visuomotor task and a resting condition. In addition it is shown for these data that the degree of sparseness and of localization can be evaluated in a strict way, provided that the data are sufficiently well described by the pairwise cross-correlations.