Evaluation of pairwise distances among orthogonal grid points in hypercube

Evaluation of pairwise distances among orthogonal grid points in hypercube

Paper in proceedings (conference paper)

This article describes an effective evaluation of pairwise distances among points that form a regular orthogonal grid inside a unit hypercube. Such an regular arrangement of points have many applications one of which is the Design of Experiments – the arrangement is known as the Full Factorial Design. The proposed process of calculation exploits the repeated point projections. Using combinatorial rules, the paper presents a closed-form exact formula that enables faster evaluation of pairwise distances and their counts compared to naive approach that enumerates the list of all possible pairs of points.

This article describes an effective evaluation of pairwise distances among points that form a regular orthogonal grid inside a unit hypercube. Such an regular arrangement of points have many applications one of which is the Design of Experiments – the arrangement is known as the Full Factorial Design. The proposed process of calculation exploits the repeated point projections. Using combinatorial rules, the paper presents a closed-form exact formula that enables faster evaluation of pairwise distances and their counts compared to naive approach that enumerates the list of all possible pairs of points.

design; orthogonal grid; pairwise distances

design; orthogonal grid; pairwise distances

SADÍLEK, V.; VOŘECHOVSKÝ, M.; MARTINÁSKOVÁ, M.

2018

21.07.2017

AMER INST PHYSICS

Melville

978-0-7354-1538-6

Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (icnaam-2016)

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http://aip.scitation.org/doi/abs/10.1063/1.4992284?journalCode=apc