A Framework for Unsupervised Selection of Indiscernibility Threshold in Rough Clustering

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Abstract

Indiscernibility threshold is a parameter in rough clustering that controls the global ability of equivalence relations for discriminating objects. During its second step, rough clustering iteratively refines equivalence relations so that the coarseness of classification of objects meets the given level of indiscernibility. However, as the relationships between this parameter and resultant clusters have not been studied yet, users should determine its value by trial and error. In this paper, we discuss the relationships between the threshold value of indiscernibility degree and clustering results, as a framework for automatic determination of indiscernibility threshold. The results showed 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.