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5.5.4 Multiple Classifier Systems with Noise
We will dispose of three well-known classifiers to build the MCS used in this illus-
trative section. SVM [ 14 ], C4.5 [ 75 ] and KNN [ 63 ] are chosen based on their good
performance in a large number of real-world problems. Moreover, they were selected
because these methods have a highly differentiated and well known noise-robustness,
which is important in order to properly evaluate the performance of MCSs in the pres-
ence of noise. Considering thec previous classifiers (SVM, C4.5 and KNN), a MCS
composed by 3 individual classifiers (SVM, C4.5 and 1-NN) is built. Therefore,
the MCSs built with heterogeneous classifiers (MCS3-1) will contain a noise-robust
algorithm (C4.5), a noise-sensitive method (SVM) and a local distance dependent
method with a low tolerance to noise (1-NN).
5.5.4.1 First Scenario: Data Sets with Class Noise
Table 5.6 shows the performance (top part of the table) and robustness (bottom part
of table) results of each classification algorithm at each noise level on data sets with
class noise. Each one of these parts in the table (performance and robustness parts)
is divided into another two parts: one with the results of the uniform class noise
Table 5.6 Performance and robustness results on data sets with class noise
Results
p-values MCS3-1 vs.
x% SVM C4.5 1-NN MCS3-1
SVM
C4.5
1-NN
0% 83.25 82.96 81.42
85.42
5.20E-03 1.80E-03 7.10E-04
10% 79.58 82.08 76.28
83
1.10E-04 3.90E-01 1.30E-07
20% 76.55 79.97 71.22
80.09
5.80E-05 9.5E-01* 1.00E-07
30% 73.82 77.9 65.88
77.1
2.80E-04 3.5E-01* 6.10E-08
40% 70.69 74.51
61
73.2
7.20E-03 2.0E-01* 7.00E-08
50% 67.07 69.22 55.55
67.64
5.40E-01 1.4E-01* 1.10E-07
0% 83.25 82.96 81.42
85.42
5.20E-03 1.80E-03 7.10E-04
10% 80.74 82.17 77.73
83.95
1.20E-04 5.80E-02 1.20E-07
20% 79.11 80.87 74.25
82.21
2.00E-04 3.50E-01 8.20E-08
30% 76.64 78.81 70.46
79.52
2.10E-03 8.20E-01 5.60E-08
40% 73.13 74.83 66.58
75.25
3.80E-02 8.0E-01* 4.50E-08
50% 65.92 60.29 63.06
64.46
2.6E-02* 2.60E-05 1.10E-01
10% 4.44
1.1
6.16
2.91
7.20E-03 1.5E-06* 1.00E-07
20% 8.16 3.78 12.1
6.4
1.50E-02 3.1E-05* 1.20E-06
30% 11.38 6.36 18.71
9.95
8.80E-02 4.6E-05* 1.80E-07
40% 15.08 10.54 24.15
14.54
6.60E-01 8.2E-05* 1.50E-06
50% 19.47
17
30.58
21.08
1.9E-01* 1.3E-04* 1.30E-05
10% 2.97
1
4.2
1.73
6.60E-03 2.0E-04* 6.70E-06
20% 4.86 2.66 8.21
3.86
7.20E-02 1.7E-03* 1.00E-05
30% 7.81 5.33 12.75
7.11
3.80E-01 2.7E-03* 6.30E-06
40% 12.01 10.19 17.2
12.08
5.50E-01 7.8E-03* 4.40E-05
50% 20.3 26.7 21.18
24.13
1.4E-04* 2.60E-03 1.1E-01*
 
 
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