Two‐dimensional projection uniformity for space‐filling designs

Abstract

We investigate a space-filling criterion based on L 2 -type discrepancies, namely the uniform projection criterion, aiming at improving designs' two-dimensional projection uniformity. Under a general reproducing kernel, we establish a formula for the uniform projection criterion function, which builds a connection between rows and columns of the design. For the commonly used discrepancies, we further use this formula to represent the two-dimensional projection uniformity in terms of the L p -distances of U-type designs. These results generalize existing works and reveal new links between the two seemingly unrelated criteria of projection uniformity and the maximin L p -distance for U-type designs. We also apply the obtained results to study several families of space-filling designs with appealing projection uniformity. Because of good projected space-filling properties, these designs are well adapted for computer experiments, especially for the case where not all the input factors are active.

Projection Uniformity of Asymmetric Fractional Factorials

“…[16] proposed the uniform projection design that have the smallest average CD values of all two-dimensional projections and are shown to have good-filling properties over all sub-spaces in terms of the distance, uniformity, and orthogonality. Based on the findings of [16], many applications and studies on uniform projection designs have emerged [17][18][19][20][21][22].…”