Geodesic Convexity and Regularized Scatter Estimators

Understand

As observed by Auderset et al.

• (2005) and Wiesel (2012), viewing covariance matrices as elements of a Riemannian manifold and using the concept of geodesic convexity provide useful tools for studying M-estimators of multivariate scatter.
• In this paper, we begin with a mathematically rigorous self-contained overview of Riemannian geometry on the space of symmetric positive definite matrices and of the notion of geodesic convexity.
• The overview contains both a review as well as new results.