We contrast three decision rules that extend Expected Utility to contexts where a convex set of probabilities is used to depict uncertainty: Γ-Maximin, Maximality, and E-admissibility. The rules extend Expected Utility theory as they require that an option is inadmissible if there is another that carries greater expected utility for each probability in a (closed) convex set. If the convex set i...

We introduce a scheme for optimally allocating a variable number of bits per LSH hyperplane. Previous approaches assign a constant number of bits per hyperplane. This neglects the fact that a subset of hyperplanes may be more informative than others. Our method, dubbed Variable Bit Quantisation (VBQ), provides a datadriven non-uniform bit allocation across hyperplanes. Despite only using a frac...

In certain classification problems, input patterns are not distributed in a clustering manner but distributed uniformly in an input space and there exist certain critical hyperplanes called decision boundaries. Since learning vector quantization (LVQ) classifies an input vector based on the nearest neighbor, the codebook vectors away from the decision boundaries are redundant. This paper presen...

We consider packings of radius r collars about hyperplanes in H. For such packings, we prove that the Delaunay cells are truncated ultra-ideal simplices which tile H. If we place n+1 hyperplanes in H each at a distance of exactly 2r to the others, we could place radius r collars about these hyperplanes. The density of these collars within the corresponding Delaunay cell is an upper bound on den...