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

Table 11

ARI values were obtained from the parameters that are given in Table 6 and were proposed by each index.

Dataset	Obtained ARI values for the each index
	SI	DI	DB	CH	S_Dbw	DSI	RMSSTD	VIASCKDE
Half-kernel	1.0000	1.0000	0.9940	1.0000	0.9153	0.9940	1.0000	1.0000
Two spirals	1.0000	1.0000	0.9804	1.0000	0.9804	1.0000	0.9990	1.0000
Outlier	1.0000	1.0000	1.0000	1.0000	0.9973	1.0000	0.8621	1.0000
Corners	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
Cluster in cluster	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.8879	1.0000
Crescent full moon	1.0000	1.0000	0.9968	1.0000	0.9105	0.9873	0.8509	1.0000
Moon	0.9379	0.6322	0.9256	0.9379	0.7874	0.7874	0.7949	0.7949
Face	0.2645	0.9949	0.9961	0.2892	0.1304	0.1226	0.8521	0.9961
Wave	0.3514	1.0000	0.1441	0.3514	0.1913	0.1441	0.0508	0.0536
Fisher iris	0.4518	0.5503	0.4518	0.4518	0.2369	0.4518	0.0106	0.5503
Breast cancer	0.8240	0.8189	0.8240	0.8240	−0.0779	−0.0779	−0.0780	0.8283
Aggregation	0.9898	0.7338	0.9898	0.9898	0.8770	0.9866	0.6330	0.9898
Thyroid	0.6715	0.6715	−0.0664	0.7339	0.2940	−0.1332	−0.1396	0.6715
Zelnik1	0.7708	1.0000	0.3409	0.7852	0.7724	0.7724	1.0000	0.7781
Zelnik5	0.9214	1.0000	0.9278	1.0000	0.9216	0.9126	0.9839	1.0000
Xclara	0.9813	0.0001	0.0001	0.9813	0.9813	0.9813	0.0001	0.9813
Banana	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
Ds2c2sc13	0.3187	0.3187	0.4911	0.4911	0.5325	0.4911	0.3187	0.5904
2sp2glob	1.0000	1.0000	0.9850	0.9940	0.9985	1.0000	0.9970	0.9940
Cure-t1-2000n	0.8850	0.8850	0.8850	0.8850	0.8850	0.8850	0.8850	0.8850