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Volume 4, Issue 3-4
Latinized, Improved LHS, and CVT Point Sets in Hypercubes

Y. Saka, M. Gunzburger & J. Burkardt

Int. J. Numer. Anal. Mod., 4 (2007), pp. 729-743.

Published online: 2007-04

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  • 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.

  • Keywords

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

  • AMS Subject Headings

62K10, 51E05, 62K05, 62L05, 62H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-729, author = {Y. Saka, M. Gunzburger and J. Burkardt}, title = {Latinized, Improved LHS, and CVT Point Sets in Hypercubes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/886.html} }
TY - JOUR T1 - Latinized, Improved LHS, and CVT Point Sets in Hypercubes AU - Y. Saka, M. Gunzburger & J. Burkardt 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 -

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.

Y. Saka, M. Gunzburger and J. Burkardt. (2007). Latinized, Improved LHS, and CVT Point Sets in Hypercubes. International Journal of Numerical Analysis and Modeling. 4 (3-4). 729-743. doi:
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