A Framework of Three-Way Cluster Analysis

A new framework of clustering is proposed inspired by the theory of three-way decisions, which is an alternative formulation different from the ones used in the existing studies. The novel three-way representation intuitively shows which objects are fringe to the cluster and it is proposed for dealing with uncertainty clustering. Instead of using two regions to represent a cluster by a single set, a cluster is represented using three regions through a pair of sets, and there are three regions such as the core region, fringe region and trivial region. A cluster is therefore more realistically characterized by a set of core objects and a set of boundary objects. In this paper, we also illustrate an algorithm for incomplete data by using the proposed evaluation-based three-way cluster model. The preliminary experimental results show that the proposed method is effective for clustering incomplete data which is one kind of uncertainty data. Furthermore, this paper reviews some three-way clustering approaches and discusses some future perspectives and potential research topics based on the three-way cluster analysis.