5 Clusters and Partitions
An important tool needed for the proof of Theorem 2.2 (part (1)) and for other results, moving forward, is to “break” up the set
into suitable clusters. This chapter discusses clustering and partitions from various points of view.
5.1 Clusters and Partitions
On an intuitive level, let us suppose that, for example, we are given a
-dimensional compact set
embedded in
and suppose one requires to produce say 10 000 points which “represent” the set
. How to do this if the set
is described by some geometric property? We may think of a process of “breaking up” a compact set roughly as a “discretization”.
Clustering and partitions of sets
with certain geometry, roughly put, are ways to “discretize” the set and are used in many mathematical subjects for example harmonic ...