Table 1.
Performance of the classifiers under the alternative hypothesis with large class-imbalance (k1 = 0.9) and moderate differences between classes (μ2 =1 )
|
Method |
λ∗a |
#, % info |
# non-info [%] |
FDR |
PA1 |
PA2 |
g-means |
AUC |
|---|---|---|---|---|---|---|---|---|
| (n1 = 90) | (n2 = 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 λθ was optimized while λγ was set to zero.