Cluster linkage

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Linkage

How the distance between two clusters is measured when deciding which two to merge next.

public enum Linkage { Ward, Complete, Average, Single }

Members — Ward merges the pair that least increases the within-cluster variance, and is the default. Complete measures the largest distance between a member of one cluster and a member of the other, Average the mean of those distances, and Single the smallest.

Example — the same five points under the two extremes, where only the height of the last merge differs.

using Lodestar.Cluster;

double[] samples = [0.0, 1.0, 5.0, 6.0, 20.0];

AgglomerativeClustering single = AgglomerativeClustering.Fit(samples, 1, 2, Linkage.Single);
AgglomerativeClustering complete = AgglomerativeClustering.Fit(samples, 1, 2, Linkage.Complete);

double nearest = single.Distances[3];     // => 14
double farthest = complete.Distances[3];  // => 20

Remarks — the choice changes the algorithm, not just the arithmetic. Single runs a minimum spanning tree and never holds a distance matrix; the other three run the nearest-neighbour chain over one, n(n − 1)/2 doubles. The two paths are the reference's own, and they break ties differently, which is why both are written rather than one generic loop.

Ward's height is a distance, not a variance: √(2·n₁n₂/(n₁+n₂)) times the distance between the two centroids, so two samples three apart merge at 3. A library that reports the increase in the sum of squares instead reports d²/2 for the same tree, and its threshold does not carry across.

Applies to — net10.0, netstandard2.0.

See also — AgglomerativeClustering, AgglomerativeClustering.Fit.

Members

Member	What it does