Cluster dbscan

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Dbscan

Finds clusters as dense regions separated by sparse ones, leaving the rest as noise.

public sealed class Dbscan

Properties — Noise is the label a sample in no dense region carries, -1. ClusterCount is how many clusters were found and FeatureCount how many values each fitted row carried. Labels is the cluster each sample belongs to (labels_), and CoreSampleIndices the rows of the core samples, ascending (core_sample_indices_).

Example — two tight pairs and one point far from both.

using Lodestar.Cluster;

// Row-major, two features per row: three points near the origin, two near (5, 5),
// and one out at (9, 9) that nothing reaches.
double[] samples = [0.0, 0.0, 0.0, 0.3, 0.3, 0.0, 5.0, 5.0, 5.0, 5.2, 9.0, 9.0];

Dbscan model = Dbscan.Fit(samples, featureCount: 2, epsilon: 0.5, minimumSamples: 2);

int clusters = model.ClusterCount;  // => 2
int first = model.Labels[0];        // => 0
int lonely = model.Labels[5];       // => -1
int cores = model.CoreSampleIndices.Count;  // => 5

Remarks — the cluster count is an output, not a question. Where KMeans is told how many clusters to find and puts every sample in one, this is told how dense a region has to be and finds however many there are — a sample in none of them is labelled Noise rather than forced into the nearest.

A core sample is one whose neighbourhood, itself included, holds at least minimumSamples samples. Every other labelled sample is a border sample: near enough to a cluster to join it, not dense enough to grow it. The distinction is what CoreSampleIndices is for, and it decides the one answer below that depends on row order.

A border sample two clusters can both reach joins whichever is grown first, which is the cluster whose lowest-indexed core sample comes first. Measured against the reference on four orderings of one point set: the label follows the growth order and not the border sample's own position, so sorting a matrix can change this answer. It is the reference's behaviour rather than a choice made here, and no other result depends on row order.

Applies to — net10.0, netstandard2.0.

See also — Dbscan.Fit, Dbscan.FitPrecomputed, KMeans, the partitioning index, clustering metrics.