présentation belief2012 9-11 mai 2012 Compiègne France

1. Combination of Supervised and Unsupervised
Classification Using Belief Function Theory
Fatma Karem(1)
Mounir Dhibi(1)
Research Unit PMI 09/UR/13-0, University campus Zarouk Gafsa 2112, Tunisia
Arnaud Martin(2)
Rennes 1 University , UMR 6074 IRISA, Street Edouard Branly BP 30219, 22302
Lannion Cedex, France
Combination of Clustering and Classification
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2. PLAN
 Problematic
 Fusion of information
 Belief Function Theory
 Proposed Approach
 Results
 Conclusion and Perspectives
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3. Classification Problems
 Many methods how to choose between them ?
 Dependance of the obtained results to the parameters initially chosen
 Incertain data manipulated sometimes missing
How to choose the
best parameters ?
Fusion between clustering and
classification
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Classification

4. Objectives of fusion
 Taking account of the complementarity of both methods
 Limitation of problems due to the choice of parameters, training
 Reduction of data and results uncertainty
 How to combine ???
 Recommendations:
 Choice of an approach treating uncertainty and imprecision
 Limitation of conflicts between clustering and classification
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Classification

5. Information Fusion
 Goal of fusion :
Combination of informations coming from different sources
Reduction of sources uncertainty and imprecision
Trying to make a compromise between the sources in order to reduce
conflict between them
Theories treating uncertainty
Exemples : theory of probability (bayesian approach), theory of possibility,
Belief Function theory (Dempster-Shafer Theory)
Combination of Clustering and
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Classification

6. Belief Function Theory (1/2)
Let Ө be a finite non empty set of elementary events to a given problem
called the frame of discernement Ө = {θi, i=1,…,n} where θi are the
hypotheses about one problem domain.
 The set of all the subsets of Ө is referred by the power set of Ө denoted
by
2θ
The impact of a piece of evidence on the different subsets of the frame
of discernment Ө is represented by the basic belief assignment (bba)
denoted by m.
 m: such that (1)
Combination of Clustering and
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7. Belief Function Theory
(2/2)
 Belief function
 Plausibility function
Combination of Clustering and
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8. New Approach (1/3)
Learning database
Clustering Classification
How to make a
compromise
between the two ?
Decision making
Combination of Clustering and
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Classification

9. New Approach (2/3)
Source 1 Source 2
Clustering Classification
clusters classes
mNS mS
Combination
Decision
making To which class belong
each object ?
Final
Decision
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Classification

10. New Approach (3/3)
How to measure our belief in the classes given by the supervised classification?
Unsupervised Supervised Step 1
Classification Classification
Probabilistic model
Computation of of Appriou
similarity between
clusters and classes
(recovery) Conjunctive Step 2
Combination
Decision making Step 3
Criterion: pignistic probability
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Classification

11. Masses computation
 Computation of mass function for the unsupervised and
supervised source
Mass computation for the
Clustering
clustering Classification
C1 C2
C2
C1
C3
C4
C6
C3
C5 C4
Recovery
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12. Computation of mass function for
the unsupervised source (1/2)
Computation of recovery
C1
C2
C3
C4
C6
Let Q={ ,i=1,…..M} : the set of classes found by the supervised classification
C={ ,i=1,…..n} : the set of classes found by the unsupervised classification
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13. Computation of mass function for
the supervised source (2/2)
With the class affected by the supervised classifier to an observation x
qi the real class
the realibilty coefficient of the supervised classification for the class
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14. Experimental Results (1/4)
Data Classification Classification
performance performance
before fusion after fusion
iris 97,33 100
Abalone 53,67 76,35
Breast-cancer 64,52 80
Haberman 75,17 100
Obtained results for KNN+FCM
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Classification

15. Experimental Results (2/4)
Data Classification Classification
performance performance
before fusion after fusion
iris 96 100
Abalone 52 79,80
Breast-cancer 96 100
Haberman 73,83 77,74
Obtained results for Bayes+FCM
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Classification

16. Experimental Results (3/4)
Data Classification Classification
performance performance
before fusion after fusion
iris 97,33 100
Abalone 53,10 78,69
Breast-cancer 64,52 80
Haberman 75,17 99,34
Obtained results for KNN+Mixture model
Combination of Clustering and
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Classification

17. Experimental Results (4/4)
Data Classification Classification
performance performance
before fusion after fusion
Iris 96 100
Abalone 52 82,45
Breast-cancer 96 100
Haberman 73,83 77,74
Obtained results for Bayes + Mixture model
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Classification

18. Conclusion and Perspectives
•Conclusions
New approach treating uncertainty and resolve conflict
 The new approach gives good results to generic data
• Perspectives
 Release of the database
 Missing data
 Real images sonar and medical images
 Improvement of the mechanism of fusion
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