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The mean over every sample, from a distance matrix you already have.

public static double ScoreFromDistances(ReadOnlySpan<int> labels, ReadOnlySpan<double> distances)

Parameters — labels gives each sample its cluster. distances is the n × n matrix row-major, so the distance from sample i to sample j is distances[(i * n) + j].

Returns — double in [-1, 1], the same number Silhouette.Score gives for the euclidean matrix of the same samples.

Exceptions — ArgumentException when the inputs disagree in size, when a distance is not finite, when a diagonal entry exceeds 100·ε — "The precomputed distance matrix contains non-zero elements on the diagonal. Use np.fill_diagonal(X, 0)." — and when the number of distinct labels falls outside [2, n - 1] — scikit-learn's own bound, carried with its own sentence: Number of labels is 1. Valid values are 2 to n_samples - 1 (inclusive). Last, a negative distance, with pairwise_distances' sentence "Negative values in data passed to pairwise_distances. Precomputed distance need to have non-negative values.." — the double space and the two stops are the reference's, and a matrix holding both a negative entry and a bad label count gets the label sentence, as scikit-learn orders them (#1275).

Example — the matrix of the two clusters above, passed in directly.

using Lodestar.Metrics;

double[] distances =
[
    0.0000, 0.1414, 7.0711, 7.2242, 7.0007,
    0.1414, 0.0000, 6.9296, 7.0824, 6.8593,
    7.0711, 6.9296, 0.0000, 0.2236, 0.1000,
    7.2242, 7.0824, 0.2236, 0.0000, 0.3162,
    7.0007, 6.8593, 0.1000, 0.3162, 0.0000,
];
int[] labels = [0, 0, 1, 1, 1];

double score = Silhouette.ScoreFromDistances(labels, distances);   // => 0.9737…

Remarks — the example's matrix is rounded to four decimals, which is why it scores 0.9737… where Silhouette.Score on the same samples scores 0.9738…. The difference is the rounding, not the method.

A name of its own rather than an overload of Silhouette.Score, because a distance matrix and a block of features are both a span of double and the two signatures would collide. A variant a parameter cannot carry gets a name, as PerOutput does on the regression metrics — here for an input rather than a return type.

Nothing checks that the matrix is a metric — symmetric, zero on the diagonal, positive elsewhere. scikit-learn does not either, and a caller who passes a similarity by mistake gets a number rather than an exception.

Applies to — net10.0, netstandard2.0.

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