An unsupervised and robust validity index for clustering analysis

The evaluation of clustering results plays an important role in clustering analysis and usually is completed by a validity index or several. But currently existing validity indexes are supervised since they greatly depend on prior information, such as specified clustering algorithms and optimal initializations. Once the prior information is unavailable, the evaluating results of these supervised validity indexes are no longer guaranteed, which lead to that their applicable ranges are greatly limited. In this paper, we firstly propose an estimation of the lower and upper bounds of the number of within-cluster distances in any dataset, and then an unsupervised validity index without needing any clustering algorithm and initialization is presented. A group of typical simulated and real datasets with various characteristics validate the proposed index in an unsupervised way. Experimental results demonstrate that the proposed index has higher accuracy in most tested datasets and has advantages in robustness and runtime compared with the other existing validity indexes.