clustering.design: Designs generated by clustering algorithms

In SFDesign: Space-Filling Designs

Designs generated by clustering algorithms

Description

This function is for producing designs by minimizing the clustering error.

Usage

clustering.design(
  n,
  p,
  X = NULL,
  D.ini = NULL,
  multi.start = 1,
  alpha = 1,
  Lloyd.iter.max = 100,
  cen.iter.max = 10,
  Lloyd.tol = 1e-04,
  cen.tol = 1e-04
)

Arguments

n	design size.
p	design dimension.
X	candidate points in [0,1]^p. If X is not provided, Sobol points is generated as cluster points.
D.ini	initial design points. If D.ini is not provided, Sobol points are generated as initial design.
multi.start	number of starting designs (cluster centers).
alpha	power of the Euclidean distance.
Lloyd.iter.max	maximum number of iterations for the Lloyd algorithm.
cen.iter.max	maximum number of iterations for the center calculation for each cluster.
Lloyd.tol	minimum relative change for the Lloyd algorithm to continue.
cen.tol	minimum relative change for the center calculation algorithm to continue.

Details

clustering.design produces a design by clustering algorithms. It minimize the clustering error (see cluster.error) by Lloyd's algorithm. When \alpha > 2, accelerated gradient descent is used to find the center for each cluster (Mak, S. and Joseph, V. R. 2018). When \alpha \leq 2: Weizfeld algorithm is used to find the center for each cluster. Let \bm{x}^{(0)}_i=\bm{x}_i denote the initial position of the ith center and and let \bm{S}_i represent the points within its Voronoi cell. The center is then updated as: \bm{x}^{(k+1)}_i = \left.\left(\sum_{\bm{s}\in\bm{S}_i}\frac{\bm{s}}{\|\bm{s}-\bm{x}^{(k)}_i\|_2^{2-\alpha}}\right)\middle/ \left(\sum_{\bm{s}\in\bm{S}_i}\frac{1}{\|\bm{s}-\bm{x}^{(k)}_i\|_2^{2-\alpha}}\right)\right. \quad \text{for } k=0, 1, \dots.

Value

design	final design points.
cluster	cluster assignment for each cluster points.
cluster.error	final cluster error.

References

Mak, S. and Joseph, V. R. (2018), “Minimax and minimax projection designs using clustering,” Journal of Computational and Graphical Statistics, 27, 166–178.

Examples

n = 20
p = 3
X = spacefillr::generate_sobol_set(1e5*p, p)
D = clustering.design(n, p, X)

SFDesign documentation built on June 22, 2025, 1:06 a.m.