Table 3.

AUROCs for various methods for selecting features

Algorithm	Parameters		Distributions
	K	α	Globally separable	Pairwise separable
Sparse PCA (Zou et al., 2006)	$K_{\text{true}}/2$	1	0.38 ± 0.21	0.97 ± 0.03
		5.75	0.59 ± 0.21	$0.93\pm 0$
		10.5	$0.48\pm \sim {10}^{-16}$	$0.93\pm 0$
		15.25	$0.5\pm 0$	0.65 ± 0.08
		20	$0.5\pm 0$	0.59 ± 0.01
	K true	1	0.47 ± 0.29	$1.0\pm 0$
		5.75	0.56 ± 0.21	$>0.99\pm \sim {10}^{-4}$
		10.5	$0.47\pm 0$	$1.0\pm 0$
		15.25	0.48 ± 0.01	0.78 ± 0.07
		20	$0.5\pm 0$	0.63 ± 0.02
	$2K_{\text{true}}$	1	0.52 ± 0.32	$1.0\pm 0$
		5.75	$0.43\pm 0$	$>0.99\pm \sim {10}^{-3}$
		10.5	$0.43\pm 0$	$1.0\pm 0$
		15.25	0.47 ± 0.01	0.80 ± 0.7
		20	$0.5\pm 0$	0.64 ± 0.01
Sparse K-means (Witten and Tibshirani, 2010)	$K_{\text{true}}/2$	1	0.80 ± 0.40	$1.0\pm \sim {10}^{-16}$
		5.75	0.84 ± 0.32	$1.0\pm 0$
		10.5	0.87 ± 0.18	$1.0\pm 0$
		15.25	0.86 ± 0.23	$1.0\pm 0$
		20	0.80 ± 0.40	$1.0\pm 0$
	K true	1	0.96 ± 0.08	$1.0\pm 0$
		5.75	0.88 ± 0.24	$1.0\pm \sim {10}^{-16}$
		10.5	0.80 ± 0.40	$1.0\pm 0$
		15.25	0.94 ± 0.12	$1.0\pm 0$
		20	$1.0\pm \sim {10}^{-16}$	$1.0\pm 0$
	$2K_{\text{true}}$	1	0.91 ± 0.18	$1.0\pm 0$
		5.75	0.85 ± 0.30	$1.0\pm 0$
		10.5	$1.0\pm ~ {10}^{-16}$	$1.0\pm 0$
		15.25	0.84 ± 0.32	$1.0\pm \sim {10}^{-16}$
		20	0.83 ± 0.34	$1.0\pm 0$
Sparse hierarchical clustering (Witten and Tibshirani, 2010)	N/A	1	0 ± 0	0.54 ± 0.03
		5.75	$0\pm 0$	0.57 ± 0.04
		10.5	$0\pm 0$	0.59 ± 0.02
		15.25	$0\pm 0$	0.56 ± 0.03
		20	$0\pm 0$	0.59 ± 0.02
LFSBSS (Li et al., 2008)	$K_{\text{true}}/2$	N/A	$0.5\pm 0$	$0.5\pm 0$
	K true		$0.5\pm 0$	$0.5\pm 0$
	$2K_{\text{true}}$		$0.5\pm 0$	$0.5\pm 0$
Spectral selection (Zhao and Liu, 2007)	N/A	N/A	$0.5\pm 0$	$0.5\pm 0$
SMD (hierarchical proposal clusters)	Unif$(2,K_{\text{true}})$	N/A	$1.0\pm \sim {10}^{-15}$	$1.0\pm 0$
	Unif$(2,2K_{\text{true}})$		1.0 ± 0.02	$1.0\pm \sim {10}^{-16}$
	Unif$(2,4K_{\text{true}})$		$1.0\pm \sim {10}^{-16}$	$1.0\pm \sim {10}^{-16}$
SMD (K-means proposal clusters)	Unif$(2,K_{\text{true}})$	N/A	$0.91\pm 0.14$	$1.0\pm 0$
	Unif$(2,2K_{\text{true}})$		0.94 ± 0.05	$1.0\pm 0$
	Unif$(2,4K_{\text{true}})$		$1.0\pm \sim {10}^{-16}$	$1.0\pm 0$

Note: Here, we generate two classes of distributions: globally separable, where one dimension separates two clusters, and other dimensions are uninformative, and pairwise separable, where each dimension separates only a pair of clusters, and the rest are uninformative. In both cases, the ratio of informative to uninformative dimensions is $D/D_s=30$. For each class of distributions, we generated 5 instances of the class, and used the algorithm in the left column to infer weights for each dimension. Some of the algorithms have input parameters, which are given in columns K (the number of clusters, or in the case of Sparse PCA, the number of components) and α (a sparsity parameter). From these weights, we calculated the AUROC score, and report the average, and standard deviation over the five trials.