Give an example of a data set consisting of three natural clusters, for which (almost always) K-means would likely find the correct clusters, but bisecting K-means would not.
What will be an ideal response?
Consider a data set that consists of three circular clusters, that are identical
in terms of the number and distribution of points, and whose centers lie on
a line and are located such that the center of the middle cluster is equally
distant from the other two. Bisecting K-means would always split the middle
cluster during its first iteration, and thus, could never produce the correct
set of clusters. (Postprocessing could be applied to address this.)
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