Improved shrunken centroid classifiers for high-dimensional class-imbalanced data

BMC Bioinformatics

Table 1 Performance of the classifiers under the alternative hypothesis with large class-imbalance ( k ₁ = 0.9 ) and moderate differences between classes ( μ ₂ =1 )

Method	λ ^∗ ^a	#, % info	# non-info [%]	FDR	PA ₁	PA ₂	g-means	AUC
					(n ₁ *= 90)*	(n ₂ *= 10)*
PAM	0.05	99.94	9184.1 [92.77]	0.99	0.95	0.11	0.31	0.6
	(0.08)	(0.87)	(1136.28)	(0.00)	(0.02)	(0.05)	(0.07)	(0.04)
GM-PAM	1.29	58.81	602.1 [6.08]	0.62	0.63	0.64	0.62	0.69
	(0.51)	(43.6)	(1004.73)	(0.38)	(0.1)	(0.16)	(0.08)	(0.1)
ALP	0.07	99.96	9004.2 [90.95]	0.99	0.95	0.11	0.3	0.61
	(0.19)	(0.54)	(2232.18)	(0.01)	(0.03)	(0.07)	(0.08)	(0.04)
GM-ALP	3.76	63.08	408.8 [4.13]	0.59	0.67	0.61	0.63	0.68
	(2.21)	(41.09)	(816.3)	(0.36)	(0.1)	(0.17)	(0.09)	(0.09)
AHP	0.36	96.89	6438.9 [65.04]	0.95	0.94	0.14	0.34	0.62
	(1.57)	(12.84)	(4235.52)	(0.11)	(0.04)	(0.1)	(0.1)	(0.05)
GM-AHP	5.29	37.45	266.5 [2.69]	0.42	0.78	0.5	0.6	0.69
	(3.94)	(37.96)	(1275.07)	(0.4)	(0.08)	(0.18)	(0.12)	(0.1)

The table reports the estimated optimal threshold (λ^∗), the number [%] of active non-informative variables (# non-info [%], selected out of 9,900 non-informative variables) and the number (also equal to %) of active informative variables (#, % info, selected out of 100 informative variables, equal to 100(1-false negative rate)), false discovery rate (FDR, # non-info/(# active)), class specific predictive accuracies, g-means and AUC, averaged over 500 repetitions; standard deviations are reported in brackets. The simulation settings are the same as in Figure 2. ^a For AHP and GM-AHP only λ_θ was optimized while λ_γ was set to zero.

ISSN: 1471-2105