In CVT, the generating point of each Voronoi cell coincides with its center of mass; CVT sampling locates the design samples at the centroids of each Voronoi cell in the input space. CVT sampling is a geometric, space-filling sampling method which is similar to k-means clustering in its simplest form.
The pysmo.sampling.CVTSampling method carries out CVT sampling. This can be done in two modes:
- The samples can be selected from a user-provided dataset, or
- The samples can be generated from a set of provided bounds.
The CVT sampling algorithm implemented here is based on McQueen's method which involves a series of random sampling and averaging steps, see http://kmh-lanl.hansonhub.com/uncertainty/meetings/gunz03vgr.pdf.
idaes.surrogate.pysmo.sampling.CVTSampling
[1] Loeven et al paper titled "A Probabilistic Radial Basis Function Approach for Uncertainty Quantification" https://pdfs.semanticscholar.org/48a0/d3797e482e37f73e077893594e01e1c667a2.pdf
[2] Centroidal Voronoi Tessellations: Applications and Algorithms by Qiang Du, Vance Faber, and Max Gunzburger https://doi.org/10.1137/S0036144599352836
[3] D. G. Loyola, M. Pedergnana, S. G. García, "Smart sampling and incremental function learning for very large high dimensional data" https://www.sciencedirect.com/science/article/pii/S0893608015001768?via%3Dihub