John Moeller

Machine Learning Researcher

Horoball Hulls and Extents in Positive Definite Space

2011-08 ADSS New York, NY
Author(s): P. Thomas Fletcher, John Moeller, Jeff M. Phillips, and Suresh Venkatasubramanian

The space of positive definite matrices P(n) is a Riemannian manifold with variable nonpositive curvature. It includes Euclidean space and hyperbolic space as submanifolds, and poses significant challenges for the design of algorithms for data analysis. In this paper, we develop foundational geometric structures and algorithms for analyzing collections of such matrices. A key technical contribution of this work is the use of horoballs, a natural generalization of halfspaces for non-positively curved Riemannian manifolds. We propose generalizations of the notion of a convex hull and a centerpoint and approximations of these structures using horoballs and based on novel decompositions of P(n). This leads to an algorithm for approximate hulls using a generalization of extents.

About

I defended my PhD thesis in Computer Science at the University of Utah School of Computing, under Suresh Venkatasubramanian. My specialties are in machine learning and algorithms. I am no longer on the market! I'll be joining Kitware in Fall of 2016.