Integrating cluster validity indices based on data envelopment analysis

Because clustering is an unsupervised learning task, a number of different validity indices have been proposed to measure the quality of the clustering results. However, there is no single best validity measure for all types of clustering tasks because individual clustering validity indices have both advantages and shortcomings. Because each validity index has demonstrated its effectiveness in particular cases, it is reasonable to expect that a more generalized clustering validity index can be developed, if individually effective cluster validity indices are appropriately integrated. In this paper, we propose a new cluster validity index, named Charnes, Cooper & Rhodes − cluster validity (CCR-CV), by integrating eight internal clustering efficiency measures based on data envelopment analysis (DEA). The proposed CCR-CV can be used for purposes that are more general because it extends the coverage of a single validity index by adaptively adjusting the combining weights of different validity indices for different datasets. Based on the experimental results on 12 artificial and 30 real datasets, the proposed clustering validity index demonstrates superior ability to determine the optimal and plausible cluster structures compared to benchmark individual validity indices.