Table 6.

Percentage of clustering object errors ($OE$) based on 1000 simulation replications when data are generated from a Euclidean space (i.e, ${\mathbb{R}}^5$) with respect to the $k$-means (K), the convex clustering (Convex), and the $k$-means++ (KPP) based on the gap statistic.

$\sigma$	$k$	$n_0=100$			$n_0=200$
		K	Convex	KPP	K	Convex	KPP
0.001	2	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$
	3	2.4	$\mathbf{0.0}$	$\mathbf{0.0}$	2.5	$\mathbf{0.0}$	$\mathbf{0.0}$
	4	4.6	0.3	$\mathbf{0.2}$	4.2	0.4	$\mathbf{0.1}$
0.002	2	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$
	3	2.4	$\mathbf{0.0}$	$\mathbf{0.0}$	2.6	$\mathbf{0.0}$	$\mathbf{0.0}$
	4	4.3	0.4	$\mathbf{0.2}$	4.3	0.4	$\mathbf{0.2}$
0.005	2	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$
	3	2.1	$\mathbf{0.0}$	$\mathbf{0.0}$	2.2	0.1	$\mathbf{0.0}$
	4	4.1	0.3	$\mathbf{0.2}$	4.5	0.4	$\mathbf{0.2}$
0.01	2	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$	$\mathbf{0.0}$
	3	2.0	0.1	$\mathbf{0.0}$	2.0	0.5	$\mathbf{0.0}$
	4	4.1	0.4	$\mathbf{0.1}$	4.3	0.4	$\mathbf{0.2}$