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Then we summarize the average misclassification rates in Table 2. Since the accuracy of class-prior estimation is improved on the mushrooms and a9a data sets, the classification accuracy is also improved. In particular, the classification results on the 20 Newsgroups data set with θP=0.7 are improved substantially. Overall, our proposed method tends to give the lower or comparable misclassification rates compared with the other methods.

Table 2:
Average Misclassification Rates (with Standard Error) on Benchmark Data Sets over 20 Trials.
PCA
Data SetθPNoned/4d/23d/4FDAPNRLPURL
ijcnn1 0.3 25.32 (1.23) 27.79 (2.05) 27.79 (2.05) 29.21 (1.30) 7.00 (0.5928.57 (2.52) 25.92 (2.64) 
 0.5 21.43 (1.22) 17.88 (1.72) 17.88 (1.72) 20.75 (1.15) 8.25 (1.3326.52 (2.26) 21.52 (1.69) 
 0.7 12.07 (0.5314.94 (1.02) 14.94 (1.02) 14.61 (1.1511.23 (1.3417.34 (1.58) 13.70 (1.04
phishing 0.3 7.41 (0.467.46 (0.487.46 (0.487.57 (0.4610.30 (2.4211.09 (0.98) 7.62 (0.45
 0.5 12.85 (2.119.75 (0.469.75 (0.469.82 (0.4024.43 (3.09) 32.02 (3.05) 10.05 (0.46
 0.7 8.07 (0.448.85 (1.088.85 (1.087.63 (0.3725.62 (1.40) 29.04 (0.73) 8.02 (0.37
mushrooms 0.3 0.73 (0.20) 1.15 (0.580.57 (0.14) 0.49 (0.141.52 (0.36) 0.24 (0.060.43 (0.09
 0.5 0.57 (0.110.57 (0.110.78 (0.160.57 (0.113.40 (0.47) 1.10 (0.243.40 (2.39
 0.7 1.42 (0.281.42 (0.281.50 (0.271.42 (0.286.38 (0.66) 1.40 (0.271.61 (0.48
a9a 0.3 24.93 (1.19) 26.49 (1.89) 26.49 (1.89) 26.20 (1.73) 21.09 (0.5926.31 (2.36) 22.32 (0.65
 0.5 30.35 (1.55) 26.07 (1.01) 26.07 (1.01) 29.52 (1.81) 22.70 (0.7727.48 (1.47) 23.70 (0.67
 0.7 20.35 (0.8020.54 (0.6120.54 (0.6119.94 (0.7819.70 (0.9720.59 (0.6019.39 (0.66
MNIST 0.3 24.58 (2.82) 17.99 (1.44) 17.99 (1.44) 22.18 (2.75) 20.92 (0.74) 12.74 (0.6311.76 (0.78
 0.5 23.00 (1.60) 22.35 (1.10) 22.35 (1.10) 23.55 (1.80) 42.10 (1.85) 15.35 (0.7518.18 (2.43
 0.7 53.34 (3.78) 52.19 (4.41) 54.42 (3.99) 53.39 (3.74) 60.86 (1.25) 16.38 (0.8418.64 (2.83
F-MNIST 0.3 14.88 (1.3018.02 (2.8618.02 (2.8615.12 (1.1819.24 (0.91) 14.54 (1.1413.54 (0.75
 0.5 13.40 (0.6912.05 (0.9612.05 (0.9613.22 (0.6237.73 (1.56) 12.15 (0.4814.10 (1.16
 0.7 9.94 (1.308.89 (0.848.89 (0.848.54 (0.8455.65 (2.14) 8.65 (0.839.29 (0.47
20 News 0.3 38.89 (3.00) 40.30 (3.64) 42.48 (3.54) 38.70 (3.81) 18.66 (0.4766.62 (1.59) 36.31 (4.13) 
 0.5 44.48 (1.82) 43.85 (2.03) 46.67 (1.15) 47.77 (0.87) 34.73 (0.8050.00 (0.00) 45.88 (1.64) 
 0.7 50.69 (0.95) 53.61 (0.73) 51.77 (1.05) 50.36 (0.83) 50.69 (0.95) 30.61 (0.5929.85 (0.13
PCA
Data SetθPNoned/4d/23d/4FDAPNRLPURL
ijcnn1 0.3 25.32 (1.23) 27.79 (2.05) 27.79 (2.05) 29.21 (1.30) 7.00 (0.5928.57 (2.52) 25.92 (2.64) 
 0.5 21.43 (1.22) 17.88 (1.72) 17.88 (1.72) 20.75 (1.15) 8.25 (1.3326.52 (2.26) 21.52 (1.69) 
 0.7 12.07 (0.5314.94 (1.02) 14.94 (1.02) 14.61 (1.1511.23 (1.3417.34 (1.58) 13.70 (1.04
phishing 0.3 7.41 (0.467.46 (0.487.46 (0.487.57 (0.4610.30 (2.4211.09 (0.98) 7.62 (0.45
 0.5 12.85 (2.119.75 (0.469.75 (0.469.82 (0.4024.43 (3.09) 32.02 (3.05) 10.05 (0.46
 0.7 8.07 (0.448.85 (1.088.85 (1.087.63 (0.3725.62 (1.40) 29.04 (0.73) 8.02 (0.37
mushrooms 0.3 0.73 (0.20) 1.15 (0.580.57 (0.14) 0.49 (0.141.52 (0.36) 0.24 (0.060.43 (0.09
 0.5 0.57 (0.110.57 (0.110.78 (0.160.57 (0.113.40 (0.47) 1.10 (0.243.40 (2.39
 0.7 1.42 (0.281.42 (0.281.50 (0.271.42 (0.286.38 (0.66) 1.40 (0.271.61 (0.48
a9a 0.3 24.93 (1.19) 26.49 (1.89) 26.49 (1.89) 26.20 (1.73) 21.09 (0.5926.31 (2.36) 22.32 (0.65
 0.5 30.35 (1.55) 26.07 (1.01) 26.07 (1.01) 29.52 (1.81) 22.70 (0.7727.48 (1.47) 23.70 (0.67
 0.7 20.35 (0.8020.54 (0.6120.54 (0.6119.94 (0.7819.70 (0.9720.59 (0.6019.39 (0.66
MNIST 0.3 24.58 (2.82) 17.99 (1.44) 17.99 (1.44) 22.18 (2.75) 20.92 (0.74) 12.74 (0.6311.76 (0.78
 0.5 23.00 (1.60) 22.35 (1.10) 22.35 (1.10) 23.55 (1.80) 42.10 (1.85) 15.35 (0.7518.18 (2.43
 0.7 53.34 (3.78) 52.19 (4.41) 54.42 (3.99) 53.39 (3.74) 60.86 (1.25) 16.38 (0.8418.64 (2.83
F-MNIST 0.3 14.88 (1.3018.02 (2.8618.02 (2.8615.12 (1.1819.24 (0.91) 14.54 (1.1413.54 (0.75
 0.5 13.40 (0.6912.05 (0.9612.05 (0.9613.22 (0.6237.73 (1.56) 12.15 (0.4814.10 (1.16
 0.7 9.94 (1.308.89 (0.848.89 (0.848.54 (0.8455.65 (2.14) 8.65 (0.839.29 (0.47
20 News 0.3 38.89 (3.00) 40.30 (3.64) 42.48 (3.54) 38.70 (3.81) 18.66 (0.4766.62 (1.59) 36.31 (4.13) 
 0.5 44.48 (1.82) 43.85 (2.03) 46.67 (1.15) 47.77 (0.87) 34.73 (0.8050.00 (0.00) 45.88 (1.64) 
 0.7 50.69 (0.95) 53.61 (0.73) 51.77 (1.05) 50.36 (0.83) 50.69 (0.95) 30.61 (0.5929.85 (0.13

Note: The boldface denotes the best and comparable approaches in terms of the average absolute error according to the t-test at the significance level 5%.

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