Minimax Clustering Designs

• Activity Number: 501
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Simon Mak*
• Keywords: space-filling designs ; optimization ; experiments ; minimax ; k-means ; particle swarm

Abstract

Minimax designs are a special class of space-filling designs which minimize the maximum distance from any point in the design region to its closest design point. Although such designs are intuitively good for computer experiments (in that it minimizes worst-case prediction error), there has been little attention devoted to developing algorithms for generating these designs. To this end, we propose a fast clustering-based heuristic by drawing an analogy to the popular Linde-Buzo-Gray algorithm in vector quantization. When compared to existing algorithms, our designs (which we call mMclust designs) give improved minimax performance, both on the unit hypercube and on general convex design regions. With a slight modification to ensure good minimax properties in all projections of the design space, we show that our mMclust designs also provide some kriging advantages over commonly-used space-filling designs.