Metrics silhouette score

Development build. This page describes main, not a released package. The latest published Lodestar.Metrics is 0.3.0 — read its documentation.

Silhouette.Score

The mean over every sample, from the samples themselves.

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

Parameters — labels gives each sample its cluster. features holds the samples row-major: sample i occupies featureCount values starting at i * featureCount. featureCount is how many values each sample holds.

Returns — double in [-1, 1]. Near 1 the clusters are well separated, near 0 they touch, and below 0 the samples are mostly closer to another cluster than to their own.

Exceptions — ArgumentException when the inputs disagree in size, 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).

Example — two clusters that are genuinely apart.

using Lodestar.Metrics;

double[] features = [0.0, 0.0, 0.1, 0.1, 5.0, 5.0, 5.1, 5.2, 5.0, 4.9];
int[] labels = [0, 0, 1, 1, 1];

double score = Silhouette.Score(labels, features, 2);   // => 0.9738…

Remarks — euclidean only. scikit-learn accepts some twenty metric= names; each one admitted here would be a parity claim to prove and keep, so a caller who wants another computes the matrix and passes it to Silhouette.ScoreFromDistances.

This is O(n²) in both time and memory: it builds the whole distance matrix and then reads it, so it allocates n² doubles of its own. ScoreFromDistances costs the same n², held by the caller instead — which is what to use when you already have the matrix, not a way to avoid paying for it. Neither runs at 100 000 samples, where the matrix is 80 GB; past about 46 000 this refuses outright, because the buffer no longer fits an array.

Applies to — net10.0, netstandard2.0.

See also — Silhouette.PerSample, Silhouette.ScoreFromDistances, the Python equivalence table.