Your SlideShare is downloading. ×
HAIS'2008: Approximate versus Linguistic Representation in Fuzzy-UCS
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

HAIS'2008: Approximate versus Linguistic Representation in Fuzzy-UCS

397

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
397
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
9
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 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

×