A comparison between conceptual clustering and conventional clustering

Clustering is a process of partitioning a given set of patterns into meaningful groups. The clustering process can be viewed as consisting of the following three phases: (i) feature selection phase, (ii) classification phase, and (iii) description generation phase. Conventional clustering algorithms implicitly use knowledge about the clustering environment to a large extent in the feature selection phase. This reduces the need for the environmental knowledge in the remaining two phases, permitting the usage of simple numerical measure of similarity in the classification phase. Conceptual clustering algorithms proposed by Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] and Stepp and Michalski [Artif. Intell., pp. 43–69 (1986)] make use of the knowledge about the clustering environment in the form of a set of predefined concepts to compute the conceptual cohesiveness during the classification phase. Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] have argued that the results obtained with the conceptual clustering algorithms are superior to conventional methods of numerical classification. However, this claim was not supported by the experimental results obtained by Dale [IEEE Trans. PAMI, PAMI-7, 241–244 (1985)]. In this paper a theoretical framework, based on an intuitively appealing set of axioms, is developed to characterize the equivalence between the conceptual clustering and conventional clustering. In other words, it is shown that any classification obtained using conceptual clustering can also be obtained using conventional clustering and vice versa.