HAIS'2008: Approximate versus Linguistic Representation in Fuzzy-UCS
1. Approximate versus Linguistic
Representation in Fuzzy-UCS
Fuzzy UCS
1Albert Orriols-Puig
2Jorge Casillas
1Ester Bernadó-Mansilla
1Enginyeria i Arquitectura La Salle, Universitat Ramon Llull
2Dpto. Ciencias de la computación e Inteligencia Artificial, Universidad de Granada
{aorriols,esterb}@salle.url.edu and casillas@decsai.ugr.es
2. Motivation
Fuzzy-UCS (Orriols-Puig, Casillas & Bernadó-Mansilla, 2008)
First Michigan-style Learning Fuzzy Classifier System
Michigan style
Evolves a population of linguistic fuzzy rules
IF x1 i small and x2 i medium or l
is ll d is large THEN class1
di l
May the linguistic rep. limit the expressiveness of Fuzzy-UCS?
Rules share the same semantics
Need of overlapping rules to predict curved boundaries
To gain expressivity:
Approximate representation. Let each variable define its own fuzzy set
IF x1 is and x2 is THEN class1
Purpose of the present work
Define an approximate rep. for Fuzzy-UCS
pp p y
Compare the approximate rep. with the linguistic rep.
Slide 2
Grup de Recerca en Sistemes Intel·ligents New Crossover Operator for Rule Discovery in XCS
3. Outline
1. Description of Fuzzy-UCS
2. Approximate Representation
3. Experimental Methodology
4. Results
5. Conclusions and Further Work
Slide 3
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
4. Description of Fuzzy-UCS
Stream of
Environment
Ei t
examples
Problem instance Match Set [M]
+
output class 1C A acc F num cs ts exp
3C A acc F num cs ts exp
5C A acc F num cs ts exp
Population [P] 6C A acc F num cs ts exp
…
1C A acc F num cs ts exp
2C A acc F num cs ts exp
3C A acc F num cs ts exp
correct set
4C A acc F num cs ts exp Classifier
generation
5C A acc F num cs ts exp
Parameters
Match set
6C A acc F num cs ts exp
Update
generation
…
Correct Set [C]
3 C A acc F num cs ts exp
Selection, reproduction,
Deletion
6 C A acc F num cs ts exp
mutation
…
IF x1 is A1k and x2 is A2k … and x is A THEN ck WITH wk
If there are no n
Genetic classfiers in [C],
n covering is k
triggered
Algorithm
Al ih
Slide 4
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
5. Description of Fuzzy-UCS
Weighted average inference (wavg)
g g ( g)
All rules vote for the class they predict according to: wk · uAk(e)
The most voted class is selected as the outputp
Action winner inference (awin)
Keep the rules that maximize wk · uAk(e) for at least, one
for, least
training example
In test, predict the class of the rule that maximizes wk · uAk(e)
test
Most numerous and fittest rules inference (nfit)
Keep the rules that maximize wk · uAk( ) · numk f at least,
(e) for,
one training example
Vote as weighted average
Slide 5
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
6. Outline
1. Description of Fuzzy-UCS
2. Approximate Representation
3. Experimental Methodology
4. Results
5. Conclusions and Further work
Slide 6
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
7. Approximate Representation
Each variable is represented by an independent fuzzy set
p y p y
IF x1 is and x2 is … and xn is THEN ck WITH wk
All the genetic operators are redefined as follows
Covering
C i
Crossover
Mutation
M tation
Slide 7
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
8. Outline
1. Description of Fuzzy-UCS
2. Approximate Representation
3. Experimental Methodology
4. Results
5. Conclusions and Further work
Slide 8
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
9. Experimental Methodology
Comparison of
C i f
Linguistic Fuzzy-UCS with 5 linguistic terms per variable with
Weighted average inference
Action winner inference
Most
M t numerous and fittest rule inference
d fitt t l i f
Approximate Fuzzy-UCS
Fuzzy UCS
Action winner inference
C4.5
As a baseline result
20 real-world problems from the UCI repository
real world
Slide 9
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
10. Experimental Methodology
Evaluation metrics (10-fold cross validation)
( )
Training accuracy
Test accuracyy
Rule set size
Statistical comparison
Friedman test
Nemenyi test
Systems configuration
N=6400, F0 = 0.99, v = 10, {θGA, θdel, θsub} = 50, Pc= 0.8, Pm= 0.04, and P# = 0.6
Linguistic Fuzzy-UCS: 5 linguistic terms per variable
Slide 10
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
11. Outline
1. Description of Fuzzy-UCS
2. Approximate Representation
3. Experimental Methodology
4. Results
5. Conclusions and Further work
Slide 11
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
12. Results
Comparison of the training accuracy
Friedman rejected the null hypothesis that all the learners
performed the same on average
Nemenyi test: CD 0 10 = 1.23
0.10
Approximate Fuzzy-UCS fits the training instances more
accurately than linguistic Fuzzy-UCS
Slide 12
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
13. Results
Does this behavior appears in test?
pp
Friedman rejected the null hypothesis that all the learners
performed the same on average
Nemenyi test CD 0 10 = 1.23
e e y test: C 0.10 3
The best learners of the comparison were:
Fuzzy-UCS wavg, awin, approximate Fuzzy-UCS and C4.5
Why approximate Fuzzy-UCS does not improve linguistic
Fuzzy-UCS?
Slide 13
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
14. Results
We observed that approximate Fuzzy-UCS may overfit
pp y y
the training instances in some specific domains
Slide 14
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
15. Results
Comparison in terms of interpretability
p p y
Friedman rejected the null hypothesis that all the learners
performed the same on average
Nemenyi test CD 0 10 = 1.23
e e y test: C 0.10 3
Fuzzy-UCS with nfit and awin evolve the most reduced rule sets
y
Still, Fuzzy-UCSa evolves large populations
Approximate representation is less legible than linguistic rep.
Slide 15
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
16. Outline
1. Description of Fuzzy-UCS
2. Approximate Representation
3. Experimental Methodology
4. Results
5. Conclusions and Further work
Slide 16
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
17. Conclusions and Further Work
Conclusions
We evidenced the advantages and disadvantages of linguistic
and approximate representation
The approximate representation enables Fuzzy-UCS to fit the
training instances more accurately
But hi improvement was not present i test
B this i in
Overfitting in some cases
Further work
Extend the comparison to two other representations
Only permit a linguistic term per variable
Hierarchic linguistic terms
g
Slide 17
Grup de Recerca en Sistemes Intel·ligents Linguistic vs. Approximate Representation in Fuzzy-UCS
18. Approximate versus Linguistic
Representation in Fuzzy-UCS
Fuzzy UCS
1Albert Orriols-Puig
2Jorge Casillas
1Ester Bernadó-Mansilla
1Enginyeria i Arquitectura La Salle, Universitat Ramon Llull
2Dpto. Ciencias de la computación e Inteligencia Artificial, Universidad de Granada
{aorriols,esterb}@salle.url.edu and casillas@decsai.ugr.es