Reducing dendrogram instability of features using rough set indiscernibility level

Cluster analysis is one of the most well known methods in data mining. One of the major problems in clustering is the dendrogram instability due to data input order. Rough set has already been used as an intelligent approach to data mining. The core concept of classical rough sets is to cluster similarities and differences of data objects based on the notions of indiscernibility and indiscernibility level. 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 quantifies the indiscernibility of pair of objects among other objects in information system and this level represents the granularity of the pairs of objects in information system. For comparison with 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 simulation shows that the hierarchical clustering yields dendrogram instability that gives different solutions under permutations of input order of data objects. The result of this paper shows that the combination of indiscernibility and its indiscernibility level plays an important role in clustering features and compared to other method, clustering based on indiscernibility and its indiscernibility level reduces the dendrogram instability.