Geometry

Biinvariant Distance Vectors

Authors: Jan Hakenberg
Comments: 10 Pages.

We construct biinvariant vector valued functions of relative distances using the influence matrix, and the Mahalanobis distance defined by scattered sets of points on Lie groups. The functions are invariant under all group operations. Distance vectors define an ordering of the points in the scattered set with respect to a group element. Applications are classification, inverse distance weighting, and the construction of generalized barycentric coordinates for the purpose of deformation, and domain transfer.
Category: Geometry