Indiscernibility degree of objects for evaluating simplicity of knowledge in the clustering procedure

This paper presents a new, rough sets-based clustering method that enables evaluation of simplicity of classification knowledge during the clustering procedure. The method iteratively refines equivalence relations so that they become more simple set of relations that give adequately coarse classification to the objects. At each step of iteration, importance of the equivalence relation is evaluated on the basis of the newly introduced measure, indiscernibility degree. An indiscernibility degree is defined as a ratio of equivalence relations that classify the two objects into the same equivalence class. If an equivalence relation has ability to discern the two objects that have high indiscernibility degree, it is considered to perform too fine classification and then modified to regard them as indiscernible objects. The refinement is repeated decreasing the threshold level of indiscernibility degree, and finally simple clusters can be obtained. Experimental results on the artificial data showed that iterative refinement of equivalence relation lead to successful generation of coarse clusters that can be represented by simple knowledge.