Positive definite matrices and the Symmetric Stein Divergence

Details Positive definite matrices and the Symmetric Stein Divergence Positive definite matrices and the Symmetric Stein Divergence

2011-10-08

arxiv.org/abs/1110.1773v1

Mathematics

Functional Analysis

15 pages

Scientific paper

Positive definite matrices arise in a dazzling variety of applications. They enjoy this ubiquity perhaps due to their rich geometric structure. In particular, positive definite matrices form a convex cone whose strict interior is also a differentiable Riemannian manifold. Building on the conic and manifold views, we advocate the \emph{Symmetric Stein Divergence} (S-Divergence) as a `natural' distance-like function on positive matrices. We motivate its naturalness in a sequence of results that connect it to the Riemannian metric on positive matrices. Going beyond, we show that the S-Divergence has many interesting properties of its own: most notably, its square-root turns out to be a metric. We discuss some properties of this metric, including Hilbert space embeddability, before concluding the paper with a list of open problems. We hope that our paper encourages others to further study the S-Divergence and its applications.

Affiliated with

Also associated with

No associations

Rating

Positive definite matrices and the Symmetric Stein Divergence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive definite matrices and the Symmetric Stein Divergence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive definite matrices and the Symmetric Stein Divergence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-87706