Clustering validity assessment using multi representatives

Clustering is a mostly unsupervised procedure and the majority of the clustering algorithms depend on certain assumptions in order to define the subgroups present in a data set. Moreover, they may behave in a different way depending on the features of the data set and their input parameters values. Therefore, in most applications the resulting clustering scheme requires some sort of evaluation as regards its validity. In this paper a new validity index, CDbw, is defined based on well-known clustering criteria enabling: i. the finding of the optimal input parameters’ values for a clustering algorithm that results in the optimal partitioning of a data set, ii. the selection of the algorithm that provides the optimal partitioning of a data set. CDbw puts emphasis on the geometric features of clusters, handling efficiently arbitrary shaped clusters. It achieves this by representing each cluster by a certain fixed number of clusters rather than a single center point. Our experimental results confirm the reliability of our index showing that it performs favorably in all cases selecting independently of clustering algorithm the scheme that best fits the data under consideration.