An efficient algorithm of generating space-filling designs with linear inequality constraints on the design region Seminar
- Time:
- 16:00
- Date:
- 21 October 2013
- Venue:
- Murray Building
For more information regarding this seminar, please email Ben Parker at B.M.Parker@southampton.ac.uk .
Event details
S3RI seminar series
Latin Hypercube designs (LHD) are in standard use as plans for deterministic computer experiments. However, these designs depend on the ability of the investigator to set each factor independently of all the others. To be specific, the implied design region for an LHD is a hypercube. However, there are cases where some parts of such a design region may be inaccessible or even nonsensical. In such cases it is useful to be able to produce a design that is both space-filling while obeying linear inequality constraints on the design region.
In this talk we present an efficient algorithm for generating space-filling designs in an arbitrary k-dimensional polytope. We first generate a random sample of a large number of points inside the polytope. Then we use a fast clustering algorithm to create n clusters of points where n is the desired number of design points. The design is then composed of the cluster centroids of each of the clusters. This construction approach leads to some desirable properties. Using the cluster centroid forces the design points away from each other in the space of the design. Using a random sample of points results in designs that do not replicate in projection. When applied to design regions without constraints, this design approach yields designs that are nearly orthogonal.
We supply several examples including designs on a simplex. We also compare our designs to maximin LHDs for various measures of space-fillingness.
Speaker information
Brad Jones , SAS/JMP