Reducing Hierarchical Clustering Instability Using Clustering Based on Indiscernibility and Indiscernibility Level

The notions of indiscernibility and discernibility are the core concept of classical rough sets to cluster similarities and differences of data objects. In this paper, we use a new method of clustering data based on the combination of indiscernibility (quantitative indiscernibility relations) and its indiscernibility level. The indiscernibility level quantify the indiscernibility of pair of objects among other objects in information systems and this level represent the granularity of pair of objects in information system. For comparison to the new method, the following four clustering methods were selected and evaluated on a simulation data set : average-, complete- and single-linkage agglomerative hierarchical clustering and Ward´s method. The result of this paper shows that the four methods of hierarchical clustering yield dendrogram instability that give different solution under permutation of input order of data object while the new method reduce dendrogram instability.