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The Davies-Bouldin index — sklearn.metrics.davies_bouldin_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, 0 or above. Lower is better, unlike every other clustering score in this package. 0 when no cluster has any spread, or when the centroids coincide.

Exceptions — ArgumentException when features is not labels.Length × featureCount, when a feature is not finite — "Input X contains NaN." or its infinity counterpart — or when the number of distinct labels is outside [2, n - 1], with scikit-learn's own sentence — the same range and the same message as CalinskiHarabasz.Score and Silhouette.Score — or when the k × k centroid distances over k clusters need more cells than one array holds, naming labels (#1480). ArgumentOutOfRangeException when featureCount is not positive.

Example — the same six samples the variance ratio scores, in the same 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 index = DaviesBouldin.Score(clusters, samples, featureCount: 2);  // => 0.2826…

Scattering the samples across three clusters makes this number rise where CalinskiHarabasz.Score makes it fall:

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 = DaviesBouldin.Score(scattered, samples, featureCount: 2);  // => 1.2713…

Remarks — a pair of clusters whose centroids coincide contributes 0 rather than an infinity: the reference substitutes infinity for the zero distance before dividing, which drops the pair out of the maximum. That is why a perfect clustering and a degenerate one can both read 0.

Euclidean only, and no precomputed-distance form, for the reason CalinskiHarabasz gives.

Applies to — net10.0, netstandard2.0.

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