Abstract

Space-filling designs are widely used in both computer and physical experiments. Column-orthogonality, maximin distance, and projection uniformity are three basic and popular space-filling criteria proposed from different perspectives, but their relationships have been rarely investigated. We show that the average squared correlation metric is a function of the pairwise L₂-distances between the rows only. We further explore the connection between uniform projection designs and maximin L₁-distance designs. Based on these connections, we develop new lower and upper bounds for column-orthogonality and projection uniformity from the perspective of distance between design points. These results not only provide new theoretical justifications for each criterion but also help in finding better space-filling designs under multiple criteria. Supplementary materials for this article are available online.

摘要

空间填充设计广泛用于计算机和物理实验。列正交性、最大距离和投影均匀性是从不同角度提出的三个基本和流行的空间填充标准，但很少研究它们的关系。我们表明，平均平方相关度量是仅行之间的成对L _{2 -距离的函数。}我们进一步探讨了均匀投影设计和 maximin L _{1之间的联系}- 距离设计。基于这些联系，我们从设计点之间的距离的角度为柱正交性和投影均匀性开发了新的下界和上界。这些结果不仅为每个标准提供了新的理论依据，而且有助于在多个标准下找到更好的空间填充设计。本文的补充材料可在线获取。