Table 1.

Percentage of numbers of clusters identified correctly ($IC$) based on 1000 simulation replications when data are generated from (26) with respect to $k$-means (K), convex clustering (Convex), the EM algorithm, and our AIC and BIC selectors in generalized $k$-means.

$\sigma$	$c$	$k$	$n_0=50$					$n_0=100$
			K	Convex	EM	AIC	BIC	K	Convex	EM	AIC	BIC
0.5	10	2	53.2	59.7	81.1	15.4	$\mathbf{97.6}$	70.2	73.9	72.4	21.4	$\mathbf{98.1}$
		3	23.3	19.2	0.0	5.6	$\mathbf{97.8}$	10.7	7.4	0.0	6.2	$\mathbf{98.9}$
	20	2	85.1	87.2	75.1	0.5	$\mathbf{88.6}$	92.3	91.7	75.2	0.3	$\mathbf{93.2}$
		3	6.7	5.6	0.0	0.0	$\mathbf{95.9}$	1.7	1.5	0.0	0.0	$\mathbf{97.3}$
1.0	10	2	22.6	25.0	75.1	17.3	$\mathbf{96.8}$	35.9	39.2	71.6	15.9	$\mathbf{98.6}$
		3	27.3	21.6	0.0	7.3	$\mathbf{95.7}$	24.4	21.5	0.0	4.9	$\mathbf{98.4}$
	20	2	52.4	52.7	74.2	0.5	$\mathbf{93.0}$	69.5	71.5	72.2	0.3	$\mathbf{93.8}$
		3	15.6	13.0	0.0	0.3	$\mathbf{87.6}$	15.1	14.0	0.0	0.0	$\mathbf{96.5}$