# Kennardstone

## Contents

### Purpose

Select a subset of samples from a data set by the Kennard-Stone algorithm.

### Synopsis

sel = kennardstone(x, k)

### Description

The KENNARDSTONE method selects a subset of samples from x which provide uniform coverage over the data set and includes samples on the boundary of the data set. The method begins by finding the two samples which are farthest apart using geometric distance. To add another sample to the selection set the algorithm selects from the remaining samples that one which has the greatest separation distance from the selected samples. The separation distance of a candidate sample from the selected set is the distance from the candidate to its closest selected sample. This most separated sample is then added to the selection set and the process is repeated until the required number of samples, k, have been added to the selection set. In practice this produces a very uniformly distributed network of selected points over the data set and includes samples along the boundary of the dataset. The method performs efficiently because it calculates the inter-sample distances matrix only once.

The method is implemented following the description published in R. W. Kennard & L. A. Stone (1969): Computer Aided Design of Experiments, Technometrics, 11:1, 137-148.

#### Inputs

• x = array, or dataset, containing data to select k samples from,
• k = number of samples to select.

#### Outputs

• sel = logical vector of length nsamples, indicating samples which are selected (true = selected). If input x was a dataset object then sel has size (1, nincluded) where nincluded is the number of included samples, and sel indicates which included samples are selected.

### Example

```>> load arch;
>> sel = kennardstone(arch, 10);
>> arch_subset = arch(sel,:);
```