Repairing uniform experimental designs: Detection and/or elimination of clusters, filling gaps

Construction of Space Filling Designs in high dimensional space remains difficult since powerful algorithms at low dimensions become difficult to use at higher dimensions that leads to non-uniform distribution in the factor space. We propose in this paper two approaches in order to repair designs: Curvilinear Component Analysis (CCA) and the Wootton, Sergent, Phan-Tan-Luu's algorithm called WSP in order to detect clusters and to fill gaps. Thus, CCA allows visualization of two or more very closely-spaced points in D dimensions by projecting them in a 2 dimensions space. Then identified clusters can be eliminated using the WSP algorithm. Moreover, the presence of gaps in input space could be very problematic since no information on the phenomenon is available and the WSP algorithm will be used in order to fill gaps by adding points in the “empty” zones. A new quality criterion has been proposed in order to follow the reparation steps. Examples in different dimensions are presented to illustrate these methods.