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uniform class noise—and also outperforms 1-NN. Therefore, the behavior of MCS3-
1 with respect to their individual components is better in the uniform scheme than
in the pairwise one.
5.5.4.2 Second Scenario: Data Sets with Attribute Noise
Table
5.7
shows the performance and robustness results of each classification algo-
rithm at each noise level on data sets with attribute noise.
At first glance we can appreciate that the results on data sets with uniform attribute
noise aremuchworse than those on data setswithGaussian noise for all the classifiers,
includingMCSs. Hence, themost disruptive attribute noise is the uniform scheme. As
the uniform attribute noise is the most disruptive noise scheme, MCS3-1 outperforms
SVM and 1-NN. However, with respect to C4.5, MCS3-1 is significantly better only
at the lowest noise levels (up to 10-15%), and is equivalent at the rest of the noise
levels. With gaussian attribute noise MCS3-1 is only better than 1-NN and SVM,
and better than C4.5 at the lowest noise levels (up to 25%).
The robustness of the MCS3-1 with uniform attribute noise does not outperform
that of its individual classifiers, as it is statistically equivalent to SVM and some-
times worse than C4.5. Regarding 1-NN, MCS3-1 performs better than 1-NN. When
Table 5.7
Performance
and robustness results on data sets with attribute 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% 81.78 81.58 78.52
83.33
3.90E-03 8.30E-02 8.10E-06
20% 78.75 79.98 75.73
80.64
4.40E-03
0.62
5.20E-06
30% 76.09 77.64 72.58
77.97
2.10E-03 9.4E-01* 1.00E-05
40% 72.75 75.19 69.58
74.84
9.90E-03 7.6E-01* 1.30E-06
50% 69.46 72.12 66.59
71.36
1.20E-02 3.1E-01* 2.70E-05
0% 83.25 82.96 81.42
85.42
5.20E-03 1.80E-03 7.10E-04
10% 82.83 82.15 80.08
84.49
3.40E-03 4.80E-03 4.00E-05
20% 81.62 81.16 78.52
83.33
4.40E-03 2.10E-02 1.00E-05
30% 80.48 80.25 76.74
81.85
1.10E-02 2.00E-01 1.00E-05
40% 78.88 78.84 74.82
80.34
1.60E-02
0.4
1.00E-05
50% 77.26 77.01 73.31
78.49
0.022
3.40E-01 3.00E-05
10% 1.38 1.68 3.63
2.4
6.7E-01* 6.6E-02* 1.30E-02
20% 5.06
3.6
6.78
5.54
6.10E-01 5.2E-03* 1.30E-02
30% 8.35 6.62 10.73
8.85
7.80E-01 2.6E-03* 1.20E-02
40% 12.13 9.6 14.29
12.44
7.8E-01* 1.1E-02* 2.00E-03
50% 16.28 13.46 17.7
16.68
8.5E-01* 3.4E-03* 2.00E-02
10% 0.25 0.94
1.6
1.03
1.70E-01 2.4E-01* 2.60E-01
20% 1.74
2.1
3.36
2.36
3.30E-01 1.2E-01* 1.00E-01
30% 3.14 3.25 5.64
4.14
7.3E-01* 1.3E-02* 7.20E-02
40% 5.23 5.02 7.91
5.93
9.40E-01 1.5E-02* 2.60E-03
50% 7.28 7.29 9.51
8.14
0.98
6.0E-02*
0.051
