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Module 5: Clustering

20267m

Given the 2D points A(1,1), B(1,2), C(2,1), D(2,2), E(8,8), F(8,9), G(9,8), H(15,15), use DBSCAN with ε = 1.5 and MinPts = 3 to identify core, border and noise points and determine the clusters.

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DBSCAN with ε = 1.5 and MinPts = 3

Assume MinPts includes the point itself. A point is core if its ε-neighborhood contains at least 3 points. Points A–D are mutually within distance (\sqrt2\approx1.414), so each has at least 4 points in its neighborhood. E, F and G are also mutually within ε (their pairwise distances are 1 or (\sqrt2)), so each has 3 points including itself. H is far from every other point.

  • Cluster 1: {A, B, C, D} — all core points.
  • Cluster 2: {E, F, G} — all core points.
  • Noise: H.
  • Border points: none.
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