Abstract
Statistical analysis of data on a Riemannian manifold extends fundamental concepts from multivariate statistical analysis in vector spaces by using the metric structure. The first example of generalizing a classical statistic to the manifold setting is the Fréchet mean, which minimizes the sum-of-squared geodesic distances to the data. Such a geometric least-squares principle also leads to extensions of principal components analysis and regression on manifolds. From these geometric concepts, we extend to a probabilistic viewpoint by defining normal distributions on Riemannian manifolds. This leads to probabilistic modeling and inference through both maximum likelihood and Bayesian approaches.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Riemannian Geometric Statistics in Medical Image Analysis
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
