Grassmannian Kernels for Efficient and Effective Detection of Group Differences in fMRI Data

Abstract

Understanding group differences in multi-subject fMRI data is essential for advancing clinical and research applications. Factorizations such as independent component analysis (ICA) and independent vector analysis (IVA) are useful for extracting components revealing group differences among subject datasets; however, the complexity of factorizations can be intractable over many datasets. To efficiently quantify group differences among datasets, we propose a simple and effective measure of dataset similarity by measuring similarity between datasets’ linear subspaces – the set of all possible components within datasets – via the Grassmannian kernel (GK) between two datasets. By comparing component subspaces and not components themselves, the GK provides a useful summary of the overall group differences existing between two datasets’ components without requiring estimation of the components, resulting in a much more computationally friendly analysis useful as a foundational step for deeper analysis (e.g., assessing whether component-level group differences exist before estimating the components in a finer-grained analysis). We validate the GK’s abilities by showing it successfully identifies meaningful group differences in several functional magnetic resonance imaging (fMRI) datasets, quantified via statistical tests on distribution differences. We further observe that the degree of group separability identified by the GK aligns closely with a detailed analysis, functional network connectivity (FNC) differences derived following application of subject-wise ICA to the datasets. We further demonstrate that in addition to detecting group differences prior to an analysis like ICA or IVA, GK can be also used to guide order selection in fMRI data.