Computing Hulls And Centerpoints In Positive Definite Space

Computer Science – Computational Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

16 pages, 2 figures

Scientific paper

In this paper, we present algorithms for computing approximate hulls and centerpoints for collections of matrices in positive definite space. There are many applications where the data under consideration, rather than being points in a Euclidean space, are positive definite (p.d.) matrices. These applications include diffusion tensor imaging in the brain, elasticity analysis in mechanical engineering, and the theory of kernel maps in machine learning. Our work centers around the notion of a horoball: the limit of a ball fixed at one point whose radius goes to infinity. Horoballs possess many (though not all) of the properties of halfspaces; in particular, they lack a strong separation theorem where two horoballs can completely partition the space. In spite of this, we show that we can compute an approximate "horoball hull" that strictly contains the actual convex hull. This approximate hull also preserves geodesic extents, which is a result of independent value: an immediate corollary is that we can approximately solve problems like the diameter and width in positive definite space. We also use horoballs to show existence of and compute approximate robust centerpoints in positive definite space, via the horoball-equivalent of the notion of depth.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Computing Hulls And Centerpoints In Positive Definite Space 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 Computing Hulls And Centerpoints In Positive Definite Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing Hulls And Centerpoints In Positive Definite Space will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-274871

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.