This paper proposes a multi-class online fuzzy classifier for dynamic environments. A fuzzy classifier comprises a set of fuzzy if-then rules where human users determine the antecedent fuzzy sets beforehand. In contrast, the consequent real values are determined by learning from training data. In an online framework, not all training dataset patterns are available beforehand. Instead, only a few patterns are available at a time step, and the subsequent patterns become available at the following time steps. The conventional online fuzzy classifier considered only two-class problems. This paper investigates the extension to the conventional fuzzy classifiers for multi-class problems. We evaluate the performance of the multi-class online fuzzy classifiers through numerical experiments on synthetic dynamic data and also several benchmark datasets.
Figures & tables
Fig. 1: Triangular membership functions.
x1
x2
Rule 1
small
small
Rule 2
small
large
Rule 3
large
small
Rule 4
large
large
TABLE I: An example of antecedent parts.
Fig. 2: Generated four fuzzy if-then rules in the example.
j
μj1(x1)
μj2(x2)
μj(x)
cj
μj(x)⋅cj
1
0.8
0.6
0.48
0.8
0.384
2
0.8
0.4
0.32
-0.2
-0.064
3
0.2
0.6
0.12
-0.4
-0.048
4
0.2
0.4
0.08
-0.7
-0.056
Total
0.216
TABLE II: Calculation of membership values.
Fig. 3: Generated boundary by the example fuzzy classifier.
Fig. 4: Don’t Care membership function.
Dataset
Instance
Class
Dim
Speaker accent recognition [ 12 ]
5473
5
10
Crabs [ 13 ]
200
5
4
Glass identification [ 12 ]
214
7
9
Iris [ 12 ]
150
3
4
Page blocks classification [ 12 ]
5473
5
10
Seeds [ 12 ]
210
3
7
TABLE III: Dataset characteristics
dataset
Fuzzy(OvR)
Fuzzy(OvO)
PA(OvR)
PA(OvO)
Delta(OvR)
Delta(OvO)
Speaker accent recognition
accuracy (%)
52.36±10.98
50.80±13.88
41.63±15.96
41.63±16.58
25.76±7.32
45.15±3.33
time (s)
314.82±1.68
267.50±0.97
1.94±0.71
1.67±0.82
2.47±0.87
2.44±0.92
Crabs
accuracy (%)
45.29±10.09
40.66±6.16
28.66±4.82
32.61±6.56
25.00±0.00
29.5±4.38
time (s)
12.90±1.21
9.96±1.24
0.76±0.67
0.68±0.67
1.04±0.67
1.04±0.70
TABLE IV: Performance comparison of Fuzzy classifier, PA, and Delta learning on benchmark datasets
Fig. 5: Distributions of petal length and petal width of the iris dataset.
Fig. 6: An overview of the area covered by the rules generated from the three-partition membership functions.
Fig. 7: The initial setup of three classes for a dynamic problem.
Fig. 8: Transitions of the important rules in f1 .
Fig. 9: Transitions of the important rules in f1,3 .
Paul G. Allen School of Computer Science and Engineering, University of Washington · Amazon · Department of Computer and Information Sciences, University of Pennsylvania