Kennard–Stone

The Kennard–Stone algorithm (Kennard & Stone, 1969) — also known as CADEX — selects a training set that covers the feature space as uniformly as possible. It is the most widely used rational splitting method for spectroscopic and tabular calibration data.

How it works

1. Compute all pairwise distances between samples.
2. Select the two samples with the largest mutual distance as the first two training points.
3. Iteratively select the sample that has the largest minimum distance to any already-selected training point (the "maximin" criterion).
4. Continue until the desired training-set size is reached.

The test set is whatever was not selected.

The result is a training set that spans the convex hull of the data — training points are spread throughout the feature space rather than clustered in any region.

When to use it

• Small to medium datasets (up to a few thousand samples) where random splits could, by chance, concentrate training and test points in the same region.
• Calibration and chemometrics — Kennard–Stone is the de facto standard for NIR, Raman, and other spectroscopic calibration splits.
• Regression when you want to avoid interpolation bias: test points near training points look easy even for a bad model.
• No target variable is needed — the split is based on X only. If you have y and want to cover both, use SPXYSplit instead.

Usage

using DataSplits

# Default Euclidean metric.
res = partition(X, KennardStoneSplit(); train = 0.8, test = 0.2)
X_train, X_test = splitdata(res, X)

# Custom metric.
using Distances
res = partition(X, KennardStoneSplit(Cityblock()); train = 70, test = 30)

# Large dataset — no full matrix in memory, but ~6× slower.
res = partition(X, LazyKennardStoneSplit(); train = 0.8, test = 0.2)

# Train / validation / test.
res = partition(X, KennardStoneSplit(), KennardStoneSplit();
                train = 70, validation = 10, test = 20)
X_tr, X_val, X_te = splitdata(res, X)

Eager vs. lazy

Limitations

• Quadratic memory for the eager variant — the N×N distance matrix is ~8 MiB at N=1000 and ~200 MiB at N=5000. Use LazyKennardStoneSplit when this does not fit in RAM, accepting ~6× slower runtime.
• Deterministic — there is no randomness, so you cannot average over multiple Kennard–Stone splits. Use MoraisLimaMartinSplit if you need stochastic variants.
• Feature scale matters — if features have very different ranges the Euclidean metric will be dominated by high-variance features. Standardise X before splitting, or use a scaled metric (e.g. WeightedEuclidean).

API reference

• KennardStoneSplit / CADEXSplit
• LazyKennardStoneSplit / LazyCADEXSplit

References

Kennard, R. W.; Stone, L. A. Computer Aided Design of Experiments. Technometrics 1969, 11(1), 137–148. https://doi.org/10.1080/00401706.1969.10490666.