Quotient Space Based Cluster Analysis1

Abstract

In the paper, the clustering is investigated under the concept of granular computing, i.e.,the framework of quotient space theory. In principle, there are mainly two kinds of similarity measurement used in cluster analysis: one for measuring the similarity among objects (data, points); the other for measuring the similarity between objects and clusters (sets of objects). Therefore, there are mainly two categories of clustering corresponding to the two measurements. Furthermore, the fuzzy clustering is gained when the fuzzy similarity measurement is used. From the granular computing point of view, all these categories of clustering can be represented by a hierarchical structure in quotient spaces. From the hierarchical structures, several new characteristics ofclustering can be obtained. It may provide a new way for further investigating clustering.