Identify the clusters in Figure 8.3 using the center-, contiguity-, and density- based definitions. Also indicate the number of clusters for each case and give a brief indication of your reasoning. Note that darkness or the number of dots indicates density. If it helps, assume center-based means K-means, contiguity-based means single link, and density-based means DBSCAN.

Question

Answer 1

(a) center-based 2 clusters. The rectangular region will be split in half.
Note that the noise is included in the two clusters.
contiguity-based 1 cluster because the two circular regions will be
joined by noise.
density-based 2 clusters, one for each circular region. Noise will be
eliminated.
(b) center-based 1 cluster that includes both rings.
contiguity-based 2 clusters, one for each rings.
density-based 2 clusters, one for each ring.
(c) center-based 3 clusters, one for each triangular region. One cluster is
also an acceptable answer.
contiguity-based 1 cluster. The three triangular regions will be joined
together because they touch.
density-based 3 clusters, one for each triangular region. Even though
the three triangles touch, the density in the region where they touch is
lower than throughout the interior of the triangles.
(d) center-based 2 clusters. The two groups of lines will be split in two.

contiguity-based 5 clusters. Each set of lines that intertwines be-
comes a cluster.

density-based 2 clusters. The two groups of lines define two regions
of high density separated by a region of low density.