Three-Way Clustering Method Based on Stability Theory

Abstract

Two-way clustering algorithms use one single set to represent a cluster, which cannot intuitively show the fringe objects of a cluster. Three-way clustering uses the core region and the fringe region to describe a cluster, which divide the universe into three disjoint sets to capture the three types of relationships between a cluster and a sample, namely, belong-to fully, belong-to partially and not belong-to fully. One of the main problems of three-way clustering is to construct the core and the fringe of each cluster. In this paper, we propose a three-way clustering algorithm by using the stability of each sample. In the proposed algorithm, we use a set of base clustering results as inputs to obtain the samples' stability by using the co-association matrix and determinacy function. With this stability, the universe is divided into the universe core and the universe fringe according to a threshold for sample's stability. The universe core is constituted by the samples with high stability and is divided into the core region of each cluster by using kmeans algorithm. Whereas the universe fringe is constituted by the samples with low stability and is assigned into the fringe region of each cluster. Therefore, a three-way explanation of the cluster is naturally formed. The experimental results on UCI data sets show that the proposed algorithm is effective in revealing cluster structures.