Multivariate distance matrix regression for a manifold-valued response variable

TL;DR

This paper introduces geometric-MDMR, a novel method that uses geodesic distances for analyzing manifold-valued data, demonstrated to outperform existing fMRI analysis techniques in simulation studies.

Contribution

The paper proposes a new manifold-aware regression method called geometric-MDMR that effectively analyzes complex data structures like brain connectivity matrices.

Findings

Geometric-MDMR outperforms current standards in fMRI analysis.

Simulation studies validate the effectiveness of the proposed method.

Manifold-aware analysis provides more interpretable results.

Abstract

In this paper, we propose the use of geodesic distances in conjunction with multivariate distance matrix regression, called geometric-MDMR, as a powerful first step analysis method for manifold-valued data. Manifold-valued data is appearing more frequently in the literature from analyses of earthquake to analysing brain patterns. Accounting for the structure of this data increases the complexity of your analysis, but allows for much more interpretable results in terms of the data. To test geometric-MDMR, we develop a method to simulate functional connectivity matrices for fMRI data to perform a simulation study, which shows that our method outperforms the current standards in fMRI analysis.