On the Nature of Degree of Indiscerniblity for Rough Clustering

In this paper, we investigate the nature of indiscernibility degree which is a primary parameter in rough clustering. Indiscernibility degree of two objects represents the ratio of equivalence relations that classify them into the same category. As it reflects the global commonality in discriminating objects, it can be associated with the coarseness of classification knowledge. Rough clustering utilizes indiscernibility degree in the process of iterative refinement of initial equivalence relations, in order to control the coarseness of the resultant clusters. However, the inference of indiscernibility degree on forming final clusters has not been well investigated, as it depends on the initial equivalence relations generated from data. In this work, we tried to seclude the influence of initial equivalence relations by introducing perfect initial equivalence relations, defined by the original class of each object, and their randomly mutated variants. Then we investigated the relationships between the threshold of indiscernibility degree and resultant clusters. The result suggested that the best range of indiscernibility degree could be determined according to the curve of indiscernibility degree and the number of clusters.