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

The paper presents a novel, rough set-based clustering method that enables the evaluation of classification knowledge simplicity during the clustering procedure. The method iteratively refines equivalence relations so that they become a more simple set of relations that give adequate coarse classification to the objects. At each step of the iteration, the 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 the ability to discern two objects that have a high indiscernibility degree, a very fine classification is performed 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 shows that iterative refinement of equivalence relation leads to successful generation of coarse clusters that can be represented by simple knowledge.