**Qi Li, Shihong Yue \*, Yaru Wang, Mingliang Ding, Jia Li and Zeying Wang**

School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China; qili\_2017@tju.edu.cn (Q.L.); yaruwang@tju.edu.cn (Y.W.); mlding@tju.edu.cn (M.D.); lijiajoyce@tju.edu.cn (J.L.); wangzeying@tju.edu.cn (Z.W.)

**\*** Correspondence: shyue1999@tju.edu.cn; Tel.: +86-22-2740-5477

Received: 11 January 2020; Accepted: 13 February 2020; Published: 16 February 2020

**Abstract:** The evaluation of clustering results plays an important role in clustering analysis. However, the existing validity indices are limited to a specific clustering algorithm, clustering parameter, and assumption in practice. In this paper, we propose a novel validity index to solve the above problems based on two complementary measures: boundary points matching and interior points connectivity. Firstly, when any clustering algorithm is performed on a dataset, we extract all boundary points for the dataset and its partitioned clusters using a nonparametric metric. The measure of boundary points matching is computed. Secondly, the interior points connectivity of both the dataset and all the partitioned clusters are measured. The proposed validity index can evaluate different clustering results on the dataset obtained from different clustering algorithms, which cannot be evaluated by the existing validity indices at all. Experimental results demonstrate that the proposed validity index can evaluate clustering results obtained by using an arbitrary clustering algorithm and find the optimal clustering parameters.

**Keywords:** clustering evaluation; clustering algorithm; cluster validity index; boundary point; interior point
