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Partitioning — Lodestar.Cluster

Three ways to group samples into clusters, each at scikit-learn parity. KMeans partitions samples into k clusters by Lloyd's algorithm, at sklearn.cluster.KMeans(algorithm="lloyd") parity. Dbscan finds however many dense regions there are and leaves the rest as noise, at sklearn.cluster.DBSCAN parity. AgglomerativeClustering builds a merge tree bottom-up and cuts it at a count or a height, at sklearn.cluster.AgglomerativeClustering parity.

The difference is what each is told. k-means is told a cluster count and puts every sample in one; DBSCAN is told how dense a region has to be, and a sample in none of them is labelled -1 rather than forced into the nearest. Agglomerative clustering is told nothing until the tree is built: one fit holds every merge, and a count or a height only decides where to cut.

Spans in, arrays out, row-major — the shape Lodestar.Metrics already uses. Labels feeds its silhouette, adjusted Rand, AMI and V-measure without being reshaped, which is the whole reason this package was cheap to make credible: the scoring half shipped first.

The starting centres are an input

k-means begins with a choice, and a choice drawn from a generator is not reproducible across two libraries. KMeansOptions.InitialCentres takes the centres themselves, and when they are given they replace the choice entirely — the move decisions/0004 made for Ω. That is what lets the oracle corpus compare every centre, label and inertia rather than comparing distributions.

Left alone, k-means++ chooses them with this package's own generator. Seed reproduces a run of Lodestar and never a run of scikit-learn, and nothing frozen depends on it.

One measured divergence

A sample exactly equidistant from two centres takes the lowest-indexed one here. decisions/0007 has the two configurations that send the reference's choice both ways, and why neither rule reproduces both.

Types

Type	What it is
KMeans	The fitted clustering: centres, labels, inertia, iterations.
KMeansOptions	Where the fit starts, and when it stops.
Dbscan	The fitted density clustering: labels, core samples, cluster count.
AgglomerativeClustering	The fitted merge tree and its cut: labels, children, merge heights.
Linkage	How the distance between two clusters is measured: Ward, complete, average or single.

One answer that depends on row order

A border sample two DBSCAN clusters can both reach joins whichever is grown first, which is the one whose lowest-indexed core sample comes first — measured against the reference on four orderings of one point set. Sorting a matrix can therefore change it, and nothing else in this package does. Dbscan.Fit states it where a caller will read it.

Two answers that depend on more than the data

Agglomerative labels are numbered by the reference's heap, not by first appearance, so two fits that agree on every cluster can still name them differently — compare clusterings with an adjusted Rand index. And where two merges are equally near, the reference's order decides the tree; it is reproduced exactly, down to the floating-point order of the distance update. AgglomerativeClustering states both.

See also

• Clustering metrics — how to score what comes out.
• Python → C# equivalence.