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The variance ratio criterion — sklearn.metrics.calinski_harabasz_score.

public static double Score(ReadOnlySpan<int> labels, ReadOnlySpan<double> features, int featureCount)

Parameters — labels is one cluster label per sample, any integers and not necessarily contiguous. features is the samples row-major: sample i occupies featureCount values from i * featureCount. featureCount is how many values each sample holds.

Returns — double, at least 0 and unbounded above; higher means the clusters are further apart relative to their own spread. 1 when the clusters have no spread at all, which the reference answers rather than dividing by zero.

Exceptions — ArgumentException when features is not labels.Length × featureCount, or when the number of distinct labels is outside [2, n - 1] — one cluster leaves nothing to compare against and one cluster per sample leaves nothing inside one. The message is scikit-learn's own, "Number of labels is k. Valid values are 2 to n_samples - 1 (inclusive)", and DaviesBouldin.Score and Silhouette.Score refuse the same range with the same sentence. ArgumentOutOfRangeException when featureCount is not positive.

Example — six samples in two dimensions, split into two clusters.

using Lodestar.Metrics;

double[] samples = [1.0, 2.0, 1.5, 1.8, 5.0, 8.0, 8.0, 8.0, 1.0, 0.6, 9.0, 11.0];
int[] clusters = [0, 0, 1, 1, 0, 1];

double ratio = CalinskiHarabasz.Score(clusters, samples, featureCount: 2);  // => 35.5865…

Splitting the same samples every which way scores far lower, which is the comparison the number is for:

using Lodestar.Metrics;

double[] samples = [1.0, 2.0, 1.5, 1.8, 5.0, 8.0, 8.0, 8.0, 1.0, 0.6, 9.0, 11.0];
int[] scattered = [0, 1, 2, 0, 1, 2];

double worse = CalinskiHarabasz.Score(scattered, samples, featureCount: 2);  // => 2.7478…

Remarks — euclidean only, as the reference is here: calinski_harabasz_score takes no metric at all, so unlike Silhouette.Score there is nothing to leave out. There is no precomputed-distance form either, because the score reads cluster centroids and a distance matrix does not carry them.

Applies to — net10.0, netstandard2.0.

See also — DaviesBouldin.Score, Silhouette.Score, the Python equivalence table.