IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
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prediction quality. This paper describes an easy methodology of finding values of parameters of
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1. Fuzzy-UCS: Preliminary Results
Albert Orriols-Puig1,2
Orriols Puig
Jorge Casillas2
Ester Bernadó-Mansilla1
1Research Group in Intelligent Systems
Enginyeria i Arquitectura La Salle, Ramon Llull University
2Dept. Computer Science and Artificial Intelligence
University of Granada
2. Motivation
Michigan-style LCSs for supervised learning. Eg. XCS and UCS
– Evolve online highly accurate models
– Competitive to the most-used machine learning techniques
• (Bernadó et al, 02; Wilson, 02; Bacardit & Butz, 04; Butz, 06; Orriols & Bernadó, 07)
Main drawback: Intepretability of the rule sets
– Number of rules or classifiers
• Reduction schemes (Wilson, 02; Fu & Davis, 02; Dixon et al., 03)
– Intervalar representation of continuous attributes: [li, ui] .
Semantic-free variables
Enginyeria i Arquitectura la Salle Slide 2
GRSI
3. Framework
Genetic Fuzzy Systems
– Change the rule representation to fuzzy rules
– Provide a robust, flexible, and powerful methodology to deal with
noisy imprecise and incomplete data
data.
noisy, imprecise,
Michigan-style Learning Fuzzy-Classifier Systems (LFCS)
– (Valenzuela-Radón, 91 & 98)
– (Parodi & Bonelli, 93)
– (Furuhashi, Nakaoka & Uchikawa, 94)
– (Velasco, 98)
– (Ishibuchi, Nakashima & Murata, 99 & 05): First LFCS for pattern classification
– (Casillas, Carse & Bull, 07) Fuzzy-XCS
Enginyeria i Arquitectura la Salle Slide 3
GRSI
4. Aim
Propose Fuzzy-UCS
– Accuracy based Michigan-style LFCS
Accuracy-based Michigan style
– Supervised learning scheme
– Derived from UCS (Bernado & Garrell, 2003)
• Introduction of a linguistic fuzzy representation
• Modification of all operators that deal with rules
– We expect:
• Achieve similar performance than UCS
• Higher interpretability since we would deal with linguistic rules
• Lower number of fuzzy rules in the final population
Enginyeria i Arquitectura la Salle Slide 4
GRSI
5. Outline
1. Description of Fuzzy-UCS
1D ii fF UCS
2.
2 Experimental Methodology
3. Results
4. Conclusions
Enginyeria i Arquitectura la Salle Slide 5
GRSI
6. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of UCS
p 3. Results
4. Conclusions
4C li
Rule representation:
– Binary variables: {0 1 #}
{0, 1,
– Continuous variables: [li, ui]
–E
Eg:
IF x1 Є [l1, u1] ^ x2 Є [l2, u2] … ^ xn Є[ln, nn] THEN class1
– Matching instance e: for all ei: li ≤ ei ≤ ui
– Set of parameters:
• Accuracy
• Fitness
• Numerosity
• Experience
• Correct set size
Enginyeria i Arquitectura la Salle Slide 6
GRSI
7. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of UCS
p 3. Results
4. Conclusions
4C li
Stream of
Environment examples
Match Set
M t h S t [M]
Problem instance
P bl it
+
output class acc F num cs ts exp
1C A
acc F num cs ts exp
3C A
Population [P] acc F num cs ts exp
5C A
acc F num cs ts exp
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 Classifier
acc F num cs ts exp generation
5C A
Parameters
acc F num cs ts exp Match set
6C A
Update
generation
…
Correct Set [C]
3 C A acc F num cs ts exp
# Correct
Deletion Selection, Reproduction,
acc =
6 C A acc F num cs ts exp
mutation
Experience
p
…
If there are no classfiers in
Fitness = accν
Genetic Algorithm [C], covering is triggered
Enginyeria i Arquitectura la Salle Slide 7
GRSI
8. Description of Fuzzy-UCS
p y
Describe the different components
1. Rule representation and matching
2. Learning interaction
3. Discovery component
3 Di t
4. Fuzzy-UCS in test mode
Enginyeria i Arquitectura la Salle Slide 8
GRSI
9. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4C li
4. Conclusions
Rule representation
– Linguistic fuzzy rules
– E.g.: IF x1 is A1 and x2 is A2 … and xn is An THEN class1
Disjunction of linguistic
fuzzy terms
– All variables share th same semantics
i bl h the ti
– Example: Ai = {small, medium, large}
IF x1 is small and x2 is medium or large THEN class1
– Codification:
IF [100 | 011] THEN class1
Enginyeria i Arquitectura la Salle Slide 9
GRSI
10. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4C li
4. Conclusions
How do we know if a given input is small, medium or large?
g p , g
– Each linguistic term defined by a membership function
Belongs to medium with a degree of 0 8
0.8
Belongs to small with a degree of 0 2
0.2
ei
Attribute value Triangular-shaped
membership functions
Enginyeria i Arquitectura la Salle Slide 10
GRSI
11. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4C li
4. Conclusions
Matching degree uAk(e)
gg () [,]
[0,1]
k: IF x1 is small and x2 is medium or large THEN class1
Example: (e1, e2)
0.8
08
0.2 0.2
e1 e2
T-conorm: bounded sum
max ( 1, 0.8 + 0.2) = 1
T-norm: product
uAk(e) = 1 * 0.2 = 0.2
Enginyeria i Arquitectura la Salle Slide 11
GRSI
12. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4. Conclusions
4C li
The role of matching changes:
• UCS: A rule matches or not an example (binary function)
• Fuzzy-UCS: A rule matches an example with a certain degree
Enginyeria i Arquitectura la Salle Slide 12
GRSI
13. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4. Conclusions
4C li
Each classifier has the following parameters:
1.
1 Weight per class wj
• Soundness with which the rule predicts the class j.
• The class value is dynamic and corresponds to the class j with higher wj
2. Fitness:
• Quality of the rule
3. Other parameters directly inherited from UCS:
• numerosity
• correct set size
• experience
Enginyeria i Arquitectura la Salle Slide 13
GRSI
14. Description of Fuzzy-UCS
p y
Describe the different components
1. Rule representation and matching
2. Learning interaction
3. Discovery component
3 Di t
4. Fuzzy-UCS in test mode
Enginyeria i Arquitectura la Salle Slide 14
GRSI
15. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4C li
4. Conclusions
Learning interaction:
– The environment provides an example e and its class c
– Match set creation: all classifiers that match with uAk(x) > 0
– Correct set creation: all classifiers that advocate c
– Covering: if there is not a classifier that maximally matches e
• Create the classifier that match the input example with maximum
degree.
• Generalize the condition with probability P#
For each variable:
A1 A2 A3
Enginyeria i Arquitectura la Salle Slide 15
GRSI
16. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4. Conclusions
4C li
Parameters’ Update
– Experience:
– Sum of correct matching per class j cmj:
Enginyeria i Arquitectura la Salle Slide 16
GRSI
17. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4. Conclusions
4C li
Parameters’ Update
– Use cm to update of the weights per each class:
• Rule that only matches instances of class c:
• wc = 1
• For all the other classes j: wj = 0
– Calculate the fitness
Pressuring toward rules that
correctly match instances of
only one class
Enginyeria i Arquitectura la Salle Slide 17
GRSI
18. Description of Fuzzy-UCS
p y
Describe the different components
1. Rule representation and matching
2. Learning interaction
3. Discovery component
3 Di t
4. Fuzzy-UCS in test mode
Enginyeria i Arquitectura la Salle Slide 18
GRSI
19. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4. Conclusions
4C li
Discovery component
– Steady state niched GA
Steady-state
– Roulette wheel selection
Instances that have a higher
g
matching degree have more
opportunities of being selected
Enginyeria i Arquitectura la Salle Slide 19
GRSI
20. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4. Conclusions
4C li
Discovery component
– Crossover and mutation applied on the antecedent
• 2 point crossover
IF [100 | 011] THEN class1
IF [101 | 100] THEN class1
• Mutation:
– Expansion
p IF [101 | 011] THEN class1
[ ]
IF [100 | 011] THEN class1
[ ]
– Contraction IF [100 | 001] THEN class1
IF [100 | 011] THEN class1
– Shift IF [010 | 011] THEN class1
IF [100 | 011] THEN class1
Enginyeria i Arquitectura la Salle Slide 20
GRSI
21. Description of Fuzzy-UCS
p y
Describe the different components
1. Rule representation and matching
2. Learning interaction
3. Discovery component
3 Di t
4. Fuzzy-UCS in test mode
Enginyeria i Arquitectura la Salle Slide 21
GRSI
22. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Description of Fuzzy-UCS
p y 3. Results
4. Conclusions
4C li
Class inference of a test example e
– Winner rule
• Inference: Select the rule that maximizes uAk(e) · Fk
• Reduction: Only keep in the final population that rules that maximize
uAk(e) · Fk at least for one training example
– Average vote
• Inference: All experienced rules vote for the class they predict. The
most voted class is returned.
Reduction: O l k
Only keep experienced rules with positive fit
i dl ith iti fitness i th
• R d ti in the
final population
Enginyeria i Arquitectura la Salle Slide 22
GRSI
24. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Results 3. Results
4. Conclusions
4C li
• 1st objective: Competitive in terms of performance
Significant difference of Fuzzy-UCS with winner rule:
Significant difference of Fuzzy-UCS with average vote:
Parameters:
iter = 100,000, N = 6,400, F0 = 0.99, v=10, {θGA, θdel, θsub} = 50,
x =0.8, u=0.04, P#=0.6, 5 linguistic labels
Enginyeria i Arquitectura la Salle Slide 24
GRSI
25. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Results 3. Results
4. Conclusions
4C li
• 2nd objective: Improve the interpretability
Example of rules evolved by UCS for iris
Example of rules evolved by Fuzzy-UCS for iris
– Linguistic terms: {XS, S, M, L, XL}
Enginyeria i Arquitectura la Salle Slide 25
GRSI
26. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Results 3. Results
4. Conclusions
4C li
Number of rules
WRule Avote UCS
80 1293 1392
bal
bl
60 1849 2075
bpa
145 4441 2265
hc
h-c
18 477 624
irs
166 3344 2908
pim
32 1142 856
thy
136 3018 1111
wbcd
101 3984 3618
wne
Enginyeria i Arquitectura la Salle Slide 26
GRSI
27. 1. Description of Fuzzy-UCS
2. Experimental Methodology
Conclusions and Further Work 3. Results
4. Conclusions
4C li
Conclusions
– We proposed a Michigan-style LFCS for supervised learning
– Competitive with respect to UCS, SMO, and C4.5
–I
Improvement in terms of interpretability with respect t UCS
ti t fi t t bilit ith t to
Further work
– Evolve more reduced populations
pp
– Enhance the comparison with new real-world problems
– Compare to other LFCS
– Exploit the incremental learning approach to dig large datasets
Enginyeria i Arquitectura la Salle Slide 27
GRSI
28. Fuzzy-UCS: Preliminary Results
Albert Orriols-Puig1,2
Orriols Puig
Jorge Casillas2
Ester Bernadó-Mansilla1
1Research Group in Intelligent Systems
Enginyeria i Arquitectura La Salle, Ramon Llull University
2Dept. Computer Science and Artificial Intelligence
University of Granada
![Motivation
Michigan-style LCSs for supervised learning. Eg. XCS and UCS
– Evolve online highly accurate models
– Competitive to the most-used machine learning techniques
• (Bernadó et al, 02; Wilson, 02; Bacardit & Butz, 04; Butz, 06; Orriols & Bernadó, 07)
Main drawback: Intepretability of the rule sets
– Number of rules or classifiers
• Reduction schemes (Wilson, 02; Fu & Davis, 02; Dixon et al., 03)
– Intervalar representation of continuous attributes: [li, ui] .
Semantic-free variables
Enginyeria i Arquitectura la Salle Slide 2
GRSI](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)