Agglomerative hierarchical clustering with dissimilarity using discernibility on attribute subsets for nominal data sets

Clustering is a method to classify given data or objects into groups called clusters using their profiles described by some attributes. In this research, we focus on cluster analysis for nominal data sets in which all attributes are nominal. For objects with nominal attributes, logical or conceptual expressions such as “attribute a equals to v” or “a is not less than v” are suitable to describe natures of clusters. However, clustering methods based on dissimilarity between a pair of objects do not necessarily output clusters of simple and compact logical expressions. To overcome the drawback, we propose new dissimilaritiy measures using discernibility of objects on attribute subsets. Discernibility is a central idea of the classical rough set theory. We apply the proposed dissimilarity measures to agglomerative hierarchical clustering, and examine characteristics of them by numerical experiments.