Knowledge-based_clustering_From Data to Information Granules.pdf

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Cover

Contents

Foreword

Preface

Clustering and Fuzzy Clustering

1.1. INTRODUCTION

1.2. BASIC NOTIONS AND NOTATION

1.2.1. Types of Data

1.2.2. Distance and Similarity

1.3. MAIN CATEGORIES OF CLUSTERING ALGORITHMS

1.3.1. Hierarchical Clustering

1.3.2. Objective Function-Based Clustering

1.4. CLUSTERING AND CLASSIFICATION

1.5. FUZZY CLUSTERING

1.6. CLUSTER VALIDITY

1.7. EXTENSIONS OF OBJECTIVE FUNCTION-BASED

1.7.1. Augmented Geometry of Fuzzy Clusters: Fuzzy C Varieties

1.7.2. Possibilistic Clustering

1.7.3. Noise Clustering

1.8. SELF-ORGANIZING MAPS AND FUZZY OBJECTIVE

1.9. CONCLUSIONS

Logic-Oriented Neurocomputing

3.1. INTRODUCTION

3.2. MAIN CATEGORIES OF FUZZY NEURONS

3.2.1. Aggregative Neurons

3.2.2. Referential (Reference) Neurons

3.3. ARCHITECTURES OF LOGIC NETWORKS

3.4. INTERPRETATION ASPECTS OF THE NETWORKS

3.5. GRANULAR INTERFACES OF LOGIC PROCESSING

3.6. CONCLUSIONS

Conditional Fuzzy Clustering

4.1. INTRODUCTION

4.2. PROBLEM STATEMENT: CONTEXT FUZZY SETS

4.3. THE OPTIMIZATION PROBLEM

4.4. COMPUTATIONAL CONSIDERATIONS

4.5. GENERALIZATIONS OF THE ALGORITHM THROUGH

4.6. FUZZY CLUSTERING WITH SPATIAL CONSTRAINTS

4.7. CONCLUSIONS

Principles of Knowledge-Based Guidance in Fuzzy Clustering

6.1. INTRODUCTION

6.2. EXAMPLES OF KNOWLEDGE-ORIENTED HINTS

6.3. THE OPTIMIZATION ENVIRONMENT

6.4. QUANTIFICATION OF KNOWLEDGE-BASED GUIDANCE HINTS

6.5. ORGANIZATION OF THE INTERACTION PROCESS

6.6. PROXIMITY-BASED CLUSTERING (P-FCM)

6.7. WEB EXPLORATION AND P-FCM

6.8. LINGUISTIC AUGMENTATION OF KNOWLEDGE-BASED HINTS

6.9. CONCLUSIONS

Collaborative Clustering

7.1. INTRODUCTION AND RATIONALE

7.2. HORIZONTAL AND VERTICAL CLUSTERING

7.3. HORIZONTAL COLLABORATIVE CLUSTERING

7.3.1. Optimization Details

7.3.2. The Flow of Computing of Collaborative Clustering

7.3.3. Quantification of the Collaborative Phenomenon of Clustering

7.4. EXPERIMENTAL STUDIES

7.5. FURTHER ENHANCEMENTS OF HORIZONTAL CLUSTERING

7.6. THE ALGORITHM OF VERTICAL CLUSTERING

7.7. A GRID MODEL OF HORIZONTAL AND VERTICAL

7.8. CONSENSUS CLUSTERING

7.9. CONCLUSIONS

Directional Clustering

8.1. INTRODUCTION

8.2. PROBLEM FORMULATION

8.2.1. The Objective Function

8.2.2. The Logic Transformation Between Information Granules

8.3. THE ALGORITHM

8.4. THE DEVELOPMENT FRAMEWORK

8.5. NUMERICAL STUDIES

8.6. CONCLUSIONS

Fuzzy Relational Clustering

9.1. INTRODUCTION AND PROBLEM STATEMENT

9.2. FCM FOR RELATIONAL DATA

9.3. DECOMPOSITION OF FUZZY RELATIONAL PATTERNS

9.3.1. Gradient-Based Solution to the Decomposition Problem

9.3.2. Neural Network Model of the Decomposition Problem

9.4. COMPARATIVE ANALYSIS

9.5. CONCLUSIONS

Fuzzy Clustering of Heterogeneous Patterns

10.1. INTRODUCTION

10.2. HETEROGENEOUS DATA

10.3. PARAMETRIC MODELS OF GRANULAR DATA

10.4. PARAMETRIC MODE OF HETEROGENEOUS

10.5. NONPARAMETRIC HETEROGENEOUS CLUSTERING

10.5.1. A Frame of Reference

10.5.2. Representation of Granular Data Through the Possibility-Necessity

10.5.3. Dereferencing

10.6. CONCLUSIONS

Hyperbox Models of Granular Data: The Tchebyschev FCM

11.1. INTRODUCTION

11.2. PROBLEM FORMULATION

11.3. THE CLUSTERING ALGORITHM—DETAILED

11.4. DEVELOPMENT OF GRANULAR PROTOTYPES

11.5. GEOMETRY OF INFORMATION GRANULES

11.6. GRANULAR DATA DESCRIPTION: A GENERAL MODEL

11.7. CONCLUSIONS

Genetic Tolerance Fuzzy Neural Networks

12.1. INTRODUCTION

12.2. OPERATIONS OF THRESHOLDING AND TOLERANCE:

12.3. TOPOLOGY OF THE LOGIC NETWORK

12.4. GENETIC OPTIMIZATION

12.5. ILLUSTRATIVE NUMERIC STUDIES

12.6. CONCLUSIONS

Granular Prototyping

13.1. INTRODUCTION

13.2. PROBLEM FORMULATION

13.2.1. Expressing Similarity Between Two Fuzzy Sets

13.2.2. Performance Index (Objective Function)

13.3. PROTOTYPE OPTIMIZATION

13.4. DEVELOPMENT OF GRANULAR PROTOTYPES

13.4.1. Optimization of the Similarity Levels

13.4.2. An Inverse Similarity Problem

13.5. CONCLUSIONS

Granular Mappings

14.1. INTRODUCTION AND PROBLEM STATEMENT

14.2. POSSIBILITY AND NECESSITY MEASURES AS THE

14.3. BUILDING THE GRANULAR MAPPING

14.4. DESIGNING MULTIVARIABLE GRANULAR MAPPINGS

14.5. QUANTIFICATION OF GRANULAR MAPPINGS

14.6. EXPERIMENTAL STUDIES

14.7. CONCLUSIONS

Linguistic Modeling

15.1. INTRODUCTION

15.2. CLUSTER-BASED REPRESENTATION

15.3. CONDITIONAL CLUSTERING IN THE DEVELOPMENT

15.4. THE GRANULAR NEURON AS A GENERIC PROCESSING

15.5. THE ARCHITECTURE OF LINGUISTIC MODELS BASED

15.6. REFINEMENTS OF LINGUISTIC MODELS

15.7. CONCLUSIONS

Bibliography

Index

KNOWLEDGE-BASEDCLUSTERINGFromDatatoInformationGranulesWitoldPedryczDepartmentofElectricalandComputerEngineeringUniversityofAlbertaEdmonton,CanadaandSystemsResearchInstitutePolishAcademyofSciencesWarsaw,PolandAJOHNWILEY&SONS,INC.,PUBLICATION

KNOWLEDGE-BASEDCLUSTERING

Copyright2005byJohnWiley&Sons,Inc.Allrightsreserved.PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.PublishedsimultaneouslyinCanada.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,thePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,(201)748-6011,fax(201)748-6008.LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsinpreparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthisbookandspeciﬁcallydisclaimanyimpliedwarrantiesofmerchantabilityorﬁtnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysalesrepresentativesorwrittensalesmaterials.Theadviceandstrategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsultwithaprofessionalwhereappropriate.Neitherthepublishernorauthorshallbeliableforanylossofproﬁtoranyothercommercialdamages,includingbutnotlimitedtospecial,incidental,consequential,orotherdamages.ForgeneralinformationonourotherproductsandservicespleasecontactourCustomerCareDepartmentwithintheU.S.at877-762-2974,outsidetheU.S.at317-572-3993orfax317-572-4002.Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprint,however,maynotbeavailableinelectronicformat.LibraryofCongressCataloging-in-PublicationData:Pedrycz,Witold,1953-Knowledge-basedclustering:fromdatatoinformationgranules/WitoldPedrycz.p.cm.“AWiley-Intersciencepublication.”Includesbibliographicalreferencesandindex.ISBN0-471-46966-1(cloth)1.Softcomputing.2.Granularcomputing.3.Fuzzysystems.I.Title.QA76.9.S63P452005006.3–dc22PrintedintheUnitedStatesofAmerica10987654321MA01923,978-750-8400,fax978-646-8600,oronthewebatwww.copyright.com.Requeststo

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