Characteristics of Indiscernibility Degree in Rough Clustering Examined Using Perfect Initial Equivalence Relations

In this paper, we analyze the influence of the indiscernibility degree, which is a primary parameter in rough clustering, on cluster formation. Rough clustering consists of two steps: (1)assignment of initial equivalence relations and (2)iterative refinement of the initial relations. Indiscernibility degree plays a key role in the second step, but it is not easy to independently analyze its characteristics because it inherits the results of step 1. In this paper, we employ the perfect initial equivalence relations, which were generated according to class labels of data, to seclude the influence of step 1. We first examine the relationship between the threshold value of indiscernibility degree and resultant clusters. After that, we apply random disturbance to the perfect relations, and examine how the result changes. The results demonstrated that the relationships between indiscernibility degree and the number of clusters draw a globally convex but multi-modal curve, and the range of indiscernibility degree that yields best cluster validity may exist on a local minimum around the global one which generates single cluster.