Hypothesis Testing For Network Data in Functional Neuroimaging

TL;DR

This paper develops a geometric and statistical framework for hypothesis testing on brain networks derived from neuroimaging data, addressing the challenge that networks are non-Euclidean objects, and demonstrates improved power over traditional methods.

Contribution

It introduces a novel geometric approach to hypothesis testing on network data, specifically using graph Laplacians and Fréchet means, applicable to functional neuroimaging.

Findings

Global network tests outperform mass-univariate approaches in power.

Method allows visualization of individual edge contributions to the test.

Framework applied to large neuroimaging datasets from the 1000 Functional Connectomes Project.

Abstract

In recent years, it has become common practice in neuroscience to use networks to summarize relational information in a set of measurements, typically assumed to be reflective of either functional or structural relationships between regions of interest in the brain. One of the most basic tasks of interest in the analysis of such data is the testing of hypotheses, in answer to questions such as "Is there a difference between the networks of these two groups of subjects?" In the classical setting, where the unit of interest is a scalar or a vector, such questions are answered through the use of familiar two-sample testing strategies. Networks, however, are not Euclidean objects, and hence classical methods do not directly apply. We address this challenge by drawing on concepts and techniques from geometry, and high-dimensional statistical inference. Our work is based on a precise geometric characterization of the space of graph Laplacian matrices and a nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate our resulting methodologies for testing in the context of networks derived from functional neuroimaging data on human subjects from the 1000 Functional Connectomes Project. In particular, we show that this global test is more statistical powerful, than a mass-univariate approach. In addition, we have also provided a method for visualizing the individual contribution of each edge to the overall test statistic.