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reasonable to visualize the rings as a single object, rather than several concentric objects.
In the case of Fig. 7.14 the choice of
(1) The fraction of the distance to the centroid that we move the representative points and
(2) The choice of how far apart representative points of two clusters need to be to avoid
merger
together determine whether we regard Fig. 7.12 as one cluster or two.
The last step of CURE is point assignment. Each point p is brought from secondary stor-
age and compared with the representative points. We assign p to the cluster of the repres-
entative point that is closest to p .
EXAMPLE 7.13 In our running example, points within the ring will surely be closer to one
of the ring's representative points than to any representative point of the circle. Likewise,
points within the circle will surely be closest to a representative point of the circle. An out-
lier - a point not within the ring or the circle - will be assigned to the ring if it is outside the
ring. If the outlier is between the ring and the circle, it will be assigned to one or the other,
somewhat favoring the ring because its representative points have been moved toward the
circle.
7.4.3
Exercises for Section 7.4
EXERCISE 7.4.1 Consider two clusters that are a circle and a surrounding ring, as in the run-
ning example of this section. Suppose:
i . The radius of the circle is c .
ii . The inner and outer circles forming the ring have radii i and o , respectively.
iii . All representative points for the two clusters are on the boundaries of the clusters.
iv . Representative points are moved 20% of the distance from their initial position toward
the centroid of their cluster.
v . Clusters are merged if, after repositioning, there are representative points from the two
clusters at distance d or less.
In terms of d , c , i , and o , under what circumstances will the ring and circle be merged into
a single cluster?
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