| Partitional clustering Component1 #292453 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. |
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  | (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 1 norm. |