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