Add Ward linkage to hierarchical clustering - #336
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Ward linkage was disabled in the parallel nearest-neighbor dendrogram
because it produced incorrect dissimilarities. Two things were missing:
* Ward's Lance-Williams recurrence needs the size of the third cluster
(the one whose distance is being updated), which differs per column of
the pairwise matrix. The other linkages only need the sizes of the two
clusters being merged, so those sizes were the only ones threaded
through merge_clades. We now also track the per-cluster sizes and pass
them to the update function.
* The recurrence runs on squared distances, so the update squares the
pairwise distances before combining them and takes the square root of
the result.
With both in place, the dissimilarities match SciPy's
scipy.cluster.hierarchy.linkage(method: "ward"). Re-enables the linkage
in fit/2, documents it, and restores the ward test.
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josevalim
approved these changes
Jul 11, 2026
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Adds
:wardlinkage support toScholar.Cluster.Hierarchical.The
ward/6update computes the new distances on squared distances, andmerge_cladesnow tracks the per-cluster sizes so the update has the size ofeach remaining cluster (which Ward needs, unlike the other linkages).
Enables
:wardinfit/2, adds it to the docs, and includes awardtestagainst the SciPy reference values.
Related to #213