Optimal number of clusters based on inter cluster elements mapping

To estimated the optimal number of clusters and evaluate the associated quality of the formed clusters is one of the major issue in cluster analysis. In this paper, we present and extend the MMM index to _nd the optimal number of clusters and their quality. The new index determines the combined mapped elements information from related clusters by comparing the occurrence of common elements across the sets of clusters from successive k number of clusters. This requires comparing the k resultant clusters in each set with respect to 'forward' and 'backward' mapping of common elements for adjacent and non-adjacent clusters (all possible distant) at all possible k. This method will also provide indicators for the similarity and overlapped (dissimilarity) of mapped elements. The optimal or best estimated number of clusters and their quality will be decided using the combination of maximum average similarity and minimum average overlap measures. The evaluation and performance of this index is illustrated and tested using real dataset.