Statistical tests for group comparison of manifold-valued data

TL;DR

This paper develops computationally efficient and geometrically appropriate statistical tests for comparing groups of data on nonlinear manifolds, motivated by Diffusion Tensor Imaging studies.

Contribution

It introduces mean-based and dispersion-based permutation tests tailored for manifold-valued data, addressing challenges in DTI analysis.

Findings

Proposes tractable permutation tests for manifold data

Ensures geometric soundness in statistical testing

Applicable to Diffusion Tensor Imaging data

Abstract

Motivated by population studies of Diffusion Tensor Imaging, the paper investigates the use of mean-based and dispersion-based permutation tests to define and compute the significance of a statistical test for data taking values on nonlinear manifolds. The paper proposes statistical tests that are computationally tractable and geometrically sound for Diffusion Tensor Imaging.