Research Article

VIASCKDE Index: A Novel Internal Cluster Validity Index for Arbitrary-Shaped Clusters Based on the Kernel Density Estimation

Table 1

Comparison of clustering validity indices that were used for experimentation in the present study.

Cluster validity IndexNotationRuntime complexityOptimal valueConsidering denser region?Handling arbitrary-shaped clusters?AdvantagesDisadvantages

Silhouette Index [30]SIMax.The score is higher when the clusters are dense and well separatedGood at handling the spherical clusters, high computational complexity
Dunn Index [31]DIMax.Competent at cluster validity taskHigh computational cost with high-dimensional data and the number of clusters
Calinski-Harabasz Index [33]CHMax.Good at well separated and compact clusters, its computational complexity is very lowIt is not competent enough at the cluster validation task.
Davies–Bouldin Index [32]DBMin.Good at well separated and compact clusters, its computational complexity is very lowIt is not competent enough at the cluster validation task.
S_Dbw validity Index [35]S_DbwMin.Its computational complexity is very lowAffected negatively by the distribution of data
Distance-based Separability Index [39]DSIMinUseful to discover the shape of clustersAffected negatively when clusters are too close and its computational complexity is high
Root-mean-square std dev [35]RMSSTDMin.Good for hierarchical clusteringHas issues when the clusters are close to each other
VIASCKDE Index (proposed)VIASCKDEMax.It can handle the arbitrary-shaped clusters, take into account the denser regions, can be used for density-based and micro-cluster-based approachesHas issues when the clusters are close to each other