Modified Mahalanobis Taguchi System for Imbalance Data Classification
Table 3
Summary of the classifiers performance ranks for all datasets.
Number
Dataset
-ratio
IR ratio
MTS
MMTS
PTM
SVM
NB
Classifier rank
LL
Med.
UL
LL
Med.
UL
LL
Med.
UL
LL
Med.
UL
LL
Med.
UL
MTS
MMTS
PTM
SVM
NB
(1)
Abalone
7.797
2088 : 1
88.02
88.91
89.52
98.31
98.77
99.22
00.00
49.20
98.40
00.00
00.00
00.00
00.00
00.00
00.00
2
1
2
3
3
(2)
Abalone
0.814
695 : 1
50.50
60.40
70.20
74.70
82.90
91.00
00.00
00.00
39.60
28.40
56.80
68.30
00.00
00.00
27.90
2
1
3
2
4
(3)
Abalone
0.661
463 : 1
56.80
61.90
67.00
72.58
75.65
76.54
21.20
42.40
43.80
29.20
51.60
66.90
00.00
00.00
00.00
2
1
3
2
4
(4)
Abalone
8.227
417 : 1
84.14
84.58
85.43
96.63
97.33
97.92
28.70
57.30
77.80
81.30
90.00
98.70
69.70
80.50
94.40
2
1
3
1
2
(5)
Abalone
1.244
347 : 1
61.00
66.70
73.80
69.30
75.70
79.80
25.80
51.40
57.80
63.40
73.60
80.70
00.00
18.80
37.10
2
1
3
2
4
(6)
Abalone
1.000
297 : 1
64.40
69.90
75.50
71.54
76.18
81.03
32.20
51.50
60.30
63.50
74.00
85.20
23.50
38.70
45.30
2
1
3
1
4
(7)
Abalone
1.019
189 : 1
71.84
73.9
76.62
72.78
77.36
80.02
18.20
35.30
44.70
70.70
76.80
83.50
13.00
25.90
44.60
1
1
2
1
2
(8)
Abalone
0.868
160 : 1
69.06
71.84
74.68
73.82
78.15
81.35
29.40
44.50
56.30
81.78
83.30
85.18
24.20
38.90
48.50
3
2
4
1
4
(9)
Abalone
0.555
130 : 1
54.07
58.1
61.82
65.14
67.88
70.21
10.90
21.90
34.00
68.90
77.40
79.90
30.63
34.25
39.62
3
2
5
1
4
(10)
ECOLI
56.509
66 : 1
84.36
86.5
88.76
98.71
99.07
99.42
99.30
99.30
99.42
99.08
99.54
99.77
0.000
0.000
28.90
3
2
2
1
4
(11)
Welding
18.837
53 : 1
57.80
65.00
71.70
79.70
89.10
98.30
79.60
86.10
92.70
38.90
69.00
89.20
38.00
67.50
84.50
2
1
1
2
3
(12)
Yeast
1.144
28 : 1
67.95
69.26
70.45
69.66
72.14
74.55
17.00
29.60
33.90
63.40
82.90
84.20
17.30
25.90
35.60
3
2
4
1
4
(13)
Shuttle
11.513
17 : 1
87.59
87.68
87.81
99.83
99.92
99.93
06.13
06.85
07.29
99.98
99.98
99.99
99.24
99.37
99.47
4
2
5
1
3
(14)
Heart
0.872
1.25 : 1
61.59
65.56
69.25
75.19
76.58
77.50
73.31
74.90
76.57
80.31
81.73
83.58
75.56
76.90
78.48
4
2
3
1
3
Fisher discriminant ratio; data overlapping index; imbalance ratio = ; MTS: Mahalanobis Taguchi System classifier at threshold = 1; MMTS: Modified Mahalanobis Taguchi System classifier; PTM: Probabilistic Mahalanobis Taguchi System classifier; SVM: Support Vector Machines classifier; NB: Naive Bayes classifier; LL: lower limit, Med.: median, and UL: upper limit based on 95% confidence interval by using one sample Wilcoxon method; [40].
