Improving Prototypes Representativeness by Internal Validity Index Analysis

Internal validity indexes are applied to evaluate the solution of a partition, which no equally reflects the same quality for all clusters, individually, in terms of prototypes representativeness. Thus, knowing their representativeness in respective clusters, it is possible adjust them to increase the confidence in analysis of found clusters. In this sense, this paper proposes a simple and effective method to obtain the internal validity index value in every cluster in a partition, identify those with low prototypes representativeness and improve them. Experiments were carried out by sum of the squared error index, which measures the compactness of clusters. The behavior of the method was illustrated by a synthetic dataset and performed for ten datasets from the literature with k-Means algorithm. The results demonstrated its effectiveness for all experiments.