Partitional Clustering

Definition

Partitional clustering decomposes a data set into a set of disjoint clusters. Given a data set of N points, a partitioning method constructs K (N ≥ K) partitions of the data, with each partition representing a cluster. That is, it classifies the data into K groups by satisfying the following requirements: (1) each group contains at least one point, and (2) each point belongs to exactly one group. Notice that for fuzzy partitioning, a point can belong to more than one group.

Many partitional clustering algorithms try to minimize an objective function. For example, in K-means and K-medoids the function (also referred to as the distortion function) is

$${\sum \limits _{i=1}^{K}}{\sum \limits _{j=1}^{\vert {C}_{i}\vert }}\mathrm{Dist}({x}_{ j},\mathrm{center}(i)),$$

(1)

where | C _i | is the number of points in cluster i, Dist(x _j , center(i)) is the distance between point x _j and center i. Many distance functions can be used, such as Euclidean distance and L...