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Fuzzy inference system and learning 08 july 2014

Fuzzy inference system and learning 08 july 2014. PLAN. Brief introduction on Fuzzy Logic and Fuzzy inference system (FIS) Real context and database Fuzzy rules and Sugeno’s classifier Implementation in three steps Visualization of FIS obtained

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Fuzzy inference system and learning 08 july 2014

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  1. Fuzzyinference system and learning08 july 2014 DataSense Digicosme | CORNEZ Laurence

  2. PLAN • Brief introduction on Fuzzy Logic and Fuzzy inference system (FIS) • Real context and database • Fuzzy rules and Sugeno’s classifier • Implementation in three steps • Visualization of FIS obtained • Perspectives in terms of intelligibility and performance DataSenseDigicosme | CORNEZ Laurence

  3. Fuzzylogic and applications • 1965, Zadeh proposes fuzzy concept : one objectcanbesimultaneously in twodifferent classes • This allows the imperfections (naturallanguage), imprecisions and uncertainties (data) • Applications (since 1974): washing machine, ABS, autofocus camera…) DataSense Digicosme | CORNEZ Laurence

  4. Fuzzy expert systems • Goal: three parts to reproduce the cognitive reasoning of an expert: • Rules base: • expression of the knowledge of the expert through « If-then » inferencerules. • directlyexpressed by expert or learnt via databases • Inputs • Inference engin able to integratetheserules and these inputs to producespecific outputs. Rules outputs inputs Inference engin DataSense Digicosme | CORNEZ Laurence

  5. Fuzzyinference system: example Rules • Rules base (Jang97) • IF temperature=lowTHEN cooling valve=half open • IF temperature=mediumTHEN cooling valve=almost open • input low half open 1 1 Implementation 0,2 0 0 T° d% medium almost open 1 1 Implementation 0,5 0 T° 0 d% 1 moteur d’inférence 18° 0 d% DataSenseDigicosme | CORNEZ Laurence 70%

  6. Work position / definition DataSense Digicosme | CORNEZ Laurence

  7. Marine explosions Quarry blasts Rock bursts Earthquakes Seismicitymap (+/- France) How to class a new eventautomaticallywith good interpretability for the expert ? DataSense Digicosme | CORNEZ Laurence

  8. Databasestutied • French seismicmetropolitan data from 1997 and 2003 • Inputs (high levelfeatures): • Hour : circular variable [0;24] • Latitude : quantitative variable [42;51] • Longitude : quantitativevariable [-5;9] • Magnitude : quantitative variable [0.7;6.0] • Date : qualitative variable with3 modalities {Workingday, Saturday, Sunday and bankholiday} • Classification output (3 possible classes): • Earthquakes (9349 events) • Quarry blasts (3485 events) • Rock bursts (1075 events) DataSense Digicosme | CORNEZ Laurence

  9. Sugeno’s classifier (normalized) defined as: Weight of the rule k An example of the input space Membership degree of x to the rule k Issue of the rule k (unit vector) Model proposed • Aggregation of rules (Sugeno order 0) -If magnitude is middle and event is nocturnal then event is earthquake -If magnitude is high then event is surely earthquake How to generate these rules automatically ? DataSense Digicosme | CORNEZ Laurence

  10. Model implementation DataSense Digicosme | CORNEZ Laurence

  11. hour magnitude Model implementation: first step(1/2) Soft Clustering = modelling class density by gaussian mixture Mountainclustering(Chiu 94) The algorithmlearns : • Gaussiannumber • Location of gaussian centers DataSense Digicosme | CORNEZ Laurence

  12. Similar good classification rates Less clusters Model implementation: first step (2/2) • Results: • Good classification rate with « winner takes all » method • 5-fold cross-validation databases What about the qualitative variable ? DataSense Digicosme | CORNEZ Laurence

  13. Associated Sugeno’s classifier With: Model implementation: second step (1/2) Probability estimations of each modalityfor each cluster DataSense Digicosme | CORNEZ Laurence

  14. Good classification rates not significantly improved Well classified point Ill classified point One cluster Model implementation: second step (2/2) Results after step II: Semi optimal (cluster juxtapositions) Not optimal (absence of clusters) DataSense Digicosme | CORNEZ Laurence

  15. Computation of new parameters: ={weights, centers and standard deviations } Model implementation: thirdstep(1/2) Improvement of parameters with EM «Expectation-Maximization »(Jordan et Jacobs 1993) • Input space is virtually augmented by adding a hidden variable, the cluster of interest • EM garantees improvement after each step DataSense Digicosme | CORNEZ Laurence

  16. Improvement for good classification rate significant improvement for cluster locations Model implementation: thirdstep(2/2) Results after step III: • 50 iterations for EM • The same 5-fold cross-validation database DataSense Digicosme | CORNEZ Laurence

  17. Rule output Weight Gaussians Estim. Proba One rule Product Class of the example One example Visualization X X X sum X Classe decided EQ [ 92.70% 0.00% 7.32%] DataSense Digicosme | CORNEZ Laurence

  18. PERSPECTIVES in terms in intelligibility and performance DataSense Digicosme | CORNEZ Laurence

  19. Comparisonwithpreviousworks • 2007 : L. Cornez • FIS 3 steps • 95,19% wellclassified • 1999 : F. Gravot • FIS - Mixture of gausians - Gradient-baseddescent • 90,5% wellclassified Intelligibility FIS 95,19% Objective FIS 90,5% • 2006 : L. Cornez • DT • 94,88% wellclassified • 95,19% wellclassified Fuzzy DT 95,19% DT 94,88% cNF+RN 92,5% cNF+MLP/SVM ~96% Performance • 1998 : S. Muller • fuzzy Controller codage • MLP • 92.5% wellclassified • 2005 : R. Quach et D. Mercier • fuzzycontroller codage • MLP : 95,9%wellclassified • SVM : 96,5% wellclassified DataSense Digicosme | CORNEZ Laurence

  20. How improveintelligibility ? According to fold cross validation database, the coverageisdifferent 20 DataSense Digicosme | CORNEZ Laurence

  21. Improveintelligibility and stability More the model is stable and more the model fit with cognitive representation more the expert canacceptit GenerativeGaussian Graph (M. Aupetit) to identifycomplex clusters DataSense Digicosme | CORNEZ Laurence

  22. Thanks ! QueStions ? Commissariat à l’énergie atomique et aux énergies alternatives Institut Carnot CEA LIST Centre de Saclay| 91191 Gif-sur-Yvette Cedex T. +33 (0)1 69 08 18 00 Etablissement public à caractère industriel et commercial | RCS Paris B 775 685 019 CEA Tech Département Métrologie, Instrumentation et InformationLaboratoire d’Analyse de Données et Intelligence des Systèmes DataSense Digicosme | CORNEZ Laurence

  23. Best fuzzydecisiontree DataSense Digicosme | CORNEZ Laurence

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