An Internal Validity Index Based on Density-Involved Distance

22 Mar 2019  ·  Lianyu Hu, Caiming Zhong ·

It is crucial to evaluate the quality of clustering results in cluster analysis. Although many cluster validity indices (CVIs) have been proposed in the literature, they have some limitations when dealing with non-spherical datasets. One reason is that the measure of cluster separation does not consider the impact of outliers and neighborhood clusters. In this paper, a new robust distance measure, one into which density is incorporated, is designed to solve the problem, and an internal validity index based on this separation measure is then proposed. This index can cope with both the spherical and non-spherical structure of clusters. The experimental results indicate that the proposed index outperforms some classical CVIs. The MATLAB code and experimental data are available at

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Task Dataset Model Metric Name Metric Value Global Rank Benchmark
Clustering Algorithms Evaluation 97 synthetic datasets CVDD HIT-THE-BEST 50 # 1
Rank difference 337 # 1
Clustering Algorithms Evaluation ionosphere CVDD Purity 0.843 # 1
Clustering Algorithms Evaluation iris CVDD Purity 0.967 # 1
Clustering Algorithms Evaluation JAFFE CVDD Purity 0.977 # 1
Clustering Algorithms Evaluation pathbased CVDD Purity 0.977 # 1
Clustering Algorithms Evaluation pixraw10P CVDD Purity 0.83 # 1
Clustering Algorithms Evaluation seeds CVDD Purity 0.905 # 1


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