Latinized, Improved LHS, and CVT Point Sets in Hypercubes

Latinized, Improved LHS, and CVT Point Sets in Hypercubes

Year:    2007

International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 729–743

Abstract

It is shown how an arbitrary set of points in the hypercube can be Latinized, i.e., can be transformed into a point set that has the Latin hypercube property. The effect of Latinization on the star discrepancy and other uniformity measures of a point set is analyzed. For a few selected but representative point sampling methods, evidence is provided to show that Latinization lowers the star discrepancy measure. A novel point sampling method is presented based on centroidal Voronoi tessellations of the hypercube. These point sets have excellent volumetric distributions, but have poor star discrepancies. Evidence is given that the Latinization of CVT points sets greatly lowers their star discrepancy measure but still preserves superior volumetric uniformity. As a result, means for determining improved Latin hypercube point samples are given.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2007-IJNAM-886

International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 3-4 : pp. 729–743

Published online:    2007-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Latin hypercube sampling quasi-Monte Carlo sampling centroidal Voronoi tessellations uniform sampling.