Interval Set Cluster Analysis: A Re-formulation

A new clustering strategy is proposed based on interval sets, which is an alternative formulation different from the ones used in the existing studies. Instead of using a single set as the representation of a cluster, each cluster is represented by an interval set that is defined by a pair of sets called the lower and upper bounds. Elements in the lower bound are typical elements of the cluster and elements between the upper and lower bounds are fringe elements of the cluster. A cluster is therefore more realistically characterized by a set of core elements and a set of boundary elements. Two types of interval set clusterings are proposed, one is non-overlapping lower bound interval set clustering and the other is overlapping lower bound interval set clusterings, corresponding to the standard partition based and covering based clusterings.