Robust Statistics on Riemannian Manifolds
Speaker: Tom Fletcher , University of Utah, SCI Institute
Date: July 2 2009
Time: 2:00PM to 3:00PM
Location: 32-D507
Host: Polina Golland, CSAIL
Contact: Polina Golland, x38005, polina@csail.mit.edu
Relevant URL: Manifold representations are useful for many different types of data,
including directional data, transformation matrices, tensors, and
shape. A popular method for estimating the centrality of such data is
the Frechet mean, which minimizes the sum-of-squared geodesic
distances. However, like the arithmetic mean in Euclidean spaces, the
Frechet mean is sensitive to outliers. In this talk I will present a
recent formulation of the geometric median, a robust measurement of
centrality, for data living in a high-dimensional Riemannian manifold.
This statistic is a generalization of the Euclidean geometric median,
sometimes known as the Fermat-Weber point. I will give proofs of
existence and uniqueness and show an algorithm for computing the
geometric median for manifold data. Finally, I will demonstrate its
usefulness on shape datasets and in robust image atlas construction.
See other events that are part of Biomedical Imaging and Analysis 2009/2010
See other events happening in July 2009
