Robust Fréchet mean and PGA on riemannian manifolds with applications to neuroimaging

Abstract

In this paper, we present novel algorithms to compute robust statistics from manifold-valued data. Specifically, we present algorithms for estimating the robust Fréchet Mean (FM) and performing a robust exact-principal geodesic analysis (ePGA) for data lying on known Riemannian manifolds. We formulate the minimization problems involved in both these problems using theminimum distance estimator called the L2E. This leads to a nonlinear optimization which is solved efficiently using a Riemannian accelerated gradient descent technique.We present competitive performance results of our algorithms applied to synthetic data with outliers, the corpus callosum shapes extracted from OASISMRI database, and diffusion MRI scans from movement disorder patients respectively.