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Tomoharu NAKASHIMA1
Takeshi SUMITANI1
Andrzej BARGIELA2
1Osaka Prefecture University, Japan; 2University of Nottingham, U.K.
A STUDY ON INCREMENTAL CONSTRUCTIONOF FUZZY RULE-BASED CLASSIFIERS
• Standard Pattern Classification• Incremental Pattern Classification• Fuzzy Rule-Based Classification• Incremental Learning of Fuzzy If-Then Rules• Computational Experiments• Conclusions
OUTLINE
All training patterns are given a priori.
It is assumed that a classifier is constructed from the given training patterns.
Typical format in supervised learning problems.
STANDARD PATTERN CLASSIFICATION
INCREMENTAL PATTERN CLASSIFICATION
A limited number of raining patterns are occasionally available.A classifier should be incrementally generated from them.
• Determine antecedent fuzzy sets• Calculate consequent part• Calculate certainty grade
FUZZY RULE-BASED CLASSIFIER
Fuzzy If-Then Rule: If x1 is A1 and x2 is A2 and … and xn is An
then Class C with CF
Incremental method A
Incremental method B
INCREMENTAL LEARNING OF FUZZY IF-THEN RULES
Update the certainty factor of fuzzy if-then rules as the weighted average of the previous sum of membership values and the new sum of membership values.
• This method considers the previously available training patterns as equally as the new training patterns
INCREMENTAL METHOD A
Update the certainty factor by using a Hebbian learning.
• The influence of previous training patterns becomes smaller as the time proceeds.
INCREMENTAL METHOD B
Two Classification Problems for pattern clasification
( Two-dimensional examples)
Static problem
Dynamic problem
COMPUTATIONAL EXPERIMENTS
STATIC PROBLEM
Class 1
Class 2Class 4
Class 3
1.00.0
1.0
x1
x2
EXPERIMENTAL RESULTS
The classification boundaries rotates with time.
DYNAMIC PROBLEM
Time 0 Time 45 Time 90
Centering at (0.5, 0.5), one degree per time step (total 360 time steps per run).
2
1
4
3
1
4
3
2
1
23
4
EXPERIMENTAL RESULTS
The incremental method A could not follow the dynamic change of the classification boundaries. This is because the method takes the previous training patterns (which are in the different class region following time steps) equally as new training patterns.The incremental method B could manage to follow the dynamic change of boundaries.
Classification boundaries generated by Incremental method B at time step 290 (i.e., the true classification boundaries have rotated 290 degrees from their original positions).
• Pattern classification with incremental availability of training patterns
• Incremental learning approach
Method A: Equal consideration of past and new training patterns
Method B: Larger weight put on new training patterns
• Experimental results
• Future works include real-world application, analysis on complexity and computational cost
CONCLUSIONS