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Cluster validity Index | Notation | Runtime complexity | Optimal value | Considering denser region? | Handling arbitrary-shaped clusters? | Advantages | Disadvantages |
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Silhouette Index [30] | SI | | Max. | ✗ | ✗ | The score is higher when the clusters are dense and well separated | Good at handling the spherical clusters, high computational complexity |
Dunn Index [31] | DI | | Max. | ✗ | ✓ | Competent at cluster validity task | High computational cost with high-dimensional data and the number of clusters |
Calinski-Harabasz Index [33] | CH | | Max. | ✗ | ✗ | Good at well separated and compact clusters, its computational complexity is very low | It is not competent enough at the cluster validation task. |
Davies–Bouldin Index [32] | DB | | Min. | ✗ | ✗ | Good at well separated and compact clusters, its computational complexity is very low | It is not competent enough at the cluster validation task. |
S_Dbw validity Index [35] | S_Dbw | | Min. | ✗ | ✓ | Its computational complexity is very low | Affected negatively by the distribution of data |
Distance-based Separability Index [39] | DSI | | Min | ✗ | ✓ | Useful to discover the shape of clusters | Affected negatively when clusters are too close and its computational complexity is high |
Root-mean-square std dev [35] | RMSSTD | | Min. | ✗ | ✗ | Good for hierarchical clustering | Has issues when the clusters are close to each other |
VIASCKDE Index (proposed) | VIASCKDE | | Max. | ✓ | ✓ | It can handle the arbitrary-shaped clusters, take into account the denser regions, can be used for density-based and micro-cluster-based approaches | Has issues when the clusters are close to each other |
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