Lecture 14 : k - center Problem

Given a set P of n points in R, a typical clustering problem asks for partitioning P into a family of k subsets {P1, . . . , Pk}, so that a certain objective function is minimized. The objective function depends on the application and varies. A typical clustering problem is the so-called centered clustering problem in which a representative point ci (or a q-flat) is chosen for each cluster Pi and the cost of the cluster pi is a function of the distances from ci to points in Pi. (e.g. max or average distance). Another example is in which the cost of a cluster Pi is a function of pairwise distances in Pi. The overall objective function is maxi μ(Pi) or ∑ i μ(Pi). In general, a clustering objective function can be viewed as ⊕ μ(Pi),