TY - JOUR
T1 - Latinized, Improved LHS, and CVT Point Sets in Hypercubes
JO - International Journal of Numerical Analysis and Modeling
VL - 3-4
SP - 729
EP - 743
PY - 2007
DA - 2007/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/886.html
KW - Latin hypercube sampling, quasi-Monte Carlo sampling, centroidal Voronoi tessellations, uniform sampling.
AB - <p style="text-align: justify;">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.</p>