Table 3.

Representative results for Simulation 5.3 (K = 5, 6, 7, 8) with N = K·50 samples. Number of replications identifying the correct number of significant clusters, mean number of significant clusters, median computing time and mean ARI over 100 replications. (K: cluster count, $\widehat{K}$: predicted cluster count, p: dimension, δ: cluster separation, F: generating distribution.)

parameters				$\left|\widehat{K}=K\right|(\text{mean}\widehat{K})$				median time (sec.)				mean ARI
K	p	δ	F	pvAU	SHCL	SHC2	BC	pv	SHCL	SHC2	BC	pvAU	SHCL	SHC2	BC
5	10	8	Gaus.	0 (8.13)	44 (4.28)	66 (4.65)	66 (4.65)	118.38	2.07	2.88	5.58	0.5	0.83	0.9	0.9
6	10	8	Gaus.	2 (6.73)	55 (5.26)	78 (5.72)	80 (5.78)	145.95	2.68	3.42	6.75	0.47	0.86	0.93	0.94
7	10	8	Gaus.	0 (7.02)	56 (6.23)	84 (6.79)	90 (6.9)	238.92	4.96	6.08	12.22	0.45	0.87	0.95	0.96
8	10	8	Gaus.	0 (5.06)	55 (6.99)	85 (7.79)	91 (7.91)	257.84	4.78	6.14	12.32	0.39	0.87	0.96	0.97
5	1000	15	Gaus.	3 (7.67)	53 (4.39)	69 (4.67)	−	623.62	111.32	125.83	−	0.22	0.86	0.9	−
6	1000	15	Gaus.	5 (8.1)	63 (5.58)	76 (5.76)	−	1014.4	136.28	146.92	−	0.33	0.91	0.93	−
7	1000	15	Gaus.	7 (8.57)	64 (6.54)	80 (6.7)	−	1294.04	184.71	198.92	−	0.37	0.92	0.94	−
8	1000	15	Gaus.	4 (8.98)	77 (7.66)	92 (7.88)	−	1620.74	262.55	279.85	−	0.41	0.95	0.97	−
5	10	8	t3	0 (42.22)	4 (2.73)	20 (3.43)	22 (7)	108.62	1.68	2.18	4.45	0.2	0.43	0.53	0.72
6	10	8	t3	0 (47.88)	9 (3.74)	26 (4.49)	20 (7.54)	178.72	2.91	3.87	9.36	0.2	0.54	0.61	0.77
7	10	8	t3	0 (63.18)	7 (4.3)	23 (5.33)	20 (8.4)	242.14	4.54	5.43	13.09	0.2	0.54	0.64	0.79
8	10	8	t3	0 (74.68)	2 (4.26)	13 (5.54)	23 (8.96)	289.16	6.24	7.38	17.53	0.17	0.46	0.58	0.8
5	1000	15	t3	20 (5.73)	13 (3.62)	10 (3.68)	−	687.27	115.76	124.45	−	0.02	0.4	0.4	−
6	1000	15	t3	15 (8.44)	4 (3.88)	8 (3.97)	−	921.06	150.42	161.42	−	0.01	0.39	0.4	−
7	1000	15	t3	7 (9.01)	10 (4.64)	12 (4.72)	−	1306.18	256.93	263.95	−	0	0.41	0.42	−
8	1000	15	t3	3 (10.07)	6 (5.53)	8 (5.7)	−	1387.78	340.85	360.39	−	0.01	0.44	0.45	−