A scalable algorithm for generating non-uniform space-filling designs

Traditional space-filling designs have long been popular to achieve uniform spread or coverage throughout the design space for diverse applications. Non-uniform space-filling (NUSF) designs were recently developed to achieve flexible densities of design points to allow users to emphasize and de-emphasize different regions of the input space. However, using a point exchange algorithm, the construction of the NUSF designs entails substantial computational costs, particularly for higher-dimensional scenarios. To improve computing efficiency and scalability, we propose a new algorithm consistent with the fundamentals of NUSF, termed Quick Non-Uniform Space-Filling (QNUSF) designs. By combining hierarchical clustering with group average linkage and strategic point selection methods, the QNUSF algorithm expedites computation. We present two point selection methods, i.e., maximin and minimax QNUSF, to achieve non-uniformity with different emphasis on the spread or coverage of the design characteristics to facilitate broader adaptability. In addition, QNUSF designs allow great flexibility for handling discrete or continuous, regular or irregular input spaces to achieve the desired density distribution and hence improve versatility and applicability for achieving different experimental goals. The computational efficiency and performance of QNUSF designs are illustrated <i>via</i> several examples.