Advances in Fuzzy Clustering and its Applications

List of Contributors xi

Foreword xv

Preface xvii

Part I Fundamentals 1

1 Fundamentals of Fuzzy Clustering 3
Rudolf Kruse, Christian Döring and Marie-Jeanne Lesot

1.1 Introduction 3

1.2 Basic Clustering Algorithms 4

1.3 Distance Function Variants 14

1.4 Objective Function Variants 18

1.5 Update Equation Variants: Alternating Cluster Estimation 25

1.6 Concluding Remarks 27

Acknowledgements 28

References 29

2 Relational Fuzzy Clustering 31
Thomas A. Runkler

2.1 Introduction 31

2.2 Object and Relational Data 31

2.3 Object Data Clustering Models 34

2.4 Relational Clustering 38

2.5 Relational Clustering with Non-spherical Prototypes 41

2.6 Relational Data Interpreted as Object Data 45

2.7 Summary 46

2.8 Experiments 46

2.9 Conclusions 49

References 50

3 Fuzzy Clustering with Minkowski Distance Functions 53
Patrick J.F. Groenen, Uzay Kaymak and Joost van Rosmalen

3.1 Introduction 53

3.2 Formalization 54

3.3 The Majorizing Algorithm for Fuzzy C-means with Minkowski Distances 56

3.4 The Effects of the Robustness Parameter l 60

3.5 Internet Attitudes 62

3.6 Conclusions 65

References 66

4 Soft Cluster Ensembles 69
Kunal Punera and Joydeep Ghosh

4.1 Introduction 69

4.2 Cluster Ensembles 71

4.3 Soft Cluster Ensembles 75

4.4 Experimental Setup 78

4.5 Soft vs. Hard Cluster Ensembles 82

4.6 Conclusions and Future Work 90

Acknowledgements 90

References 90

Part II Visualization 93

5 Aggregation and Visualization of Fuzzy Clusters Based on Fuzzy Similarity Measures 95
János Abonyi and Balázs Feil

5.1 Problem Definition 97

5.2 Classical Methods for Cluster Validity and Merging 99

5.3 Similarity of Fuzzy Clusters 100

5.4 Visualization of Clustering Results 103

5.5 Conclusions 116

Appendix 5A.1 Validity Indices 117

Appendix 5A.2 The Modified Sammon Mapping Algorithm 120

Acknowledgements 120

References 120

6 Interactive Exploration of Fuzzy Clusters 123
Bernd Wiswedel, David E. Patterson and Michael R. Berthold

6.1 Introduction 123

6.2 Neighborgram Clustering 125

6.3 Interactive Exploration 131

6.4 Parallel Universes 135

6.5 Discussion 136

References 136

Part III Algorithms and Computational Aspects 137

7 Fuzzy Clustering with Participatory Learning and Applications 139
Leila Roling Scariot da Silva, Fernando Gomide and Ronald Yager

7.1 Introduction 139

7.2 Participatory Learning 140

7.3 Participatory Learning in Fuzzy Clustering 142

7.4 Experimental Results 145

7.5 Applications 148

7.6 Conclusions 152

Acknowledgements 152

References 152

8 Fuzzy Clustering of Fuzzy Data 155
Pierpaolo D’Urso

8.1 Introduction 155

8.2 Informational Paradigm, Fuzziness and Complexity in Clustering Processes 156

8.3 Fuzzy Data 160

8.4 Fuzzy Clustering of Fuzzy Data 165

8.5 An Extension: Fuzzy Clustering Models for Fuzzy Data Time Arrays 176

8.6 Applicative Examples 180

8.7 Concluding Remarks and Future Perspectives 187

References 189

9 Inclusion-based Fuzzy Clustering 193
Samia Nefti-Meziani and Mourad Oussalah

9.1 Introduction 193

9.2 Background: Fuzzy Clustering 195

9.3 Construction of an Inclusion Index 196

9.4 Inclusion-based Fuzzy Clustering 198

9.5 Numerical Examples and Illustrations 201

9.6 Conclusions 206

Acknowledgements 206

Appendix 9A.1 207

References 208

10 Mining Diagnostic Rules Using Fuzzy Clustering 211
Giovanna Castellano, Anna M. Fanelli and Corrado Mencar

10.1 Introduction 211

10.2 Fuzzy Medical Diagnosis 212

10.3 Interpretability in Fuzzy Medical Diagnosis 213

10.4 A Framework for Mining Interpretable Diagnostic Rules 216

10.5 An Illustrative Example 221

10.6 Concluding Remarks 226

References 226

11 Fuzzy Regression Clustering 229
Mikal Sato-Ilic

11.1 Introduction 229

11.2 Statistical Weighted Regression Models 230

11.3 Fuzzy Regression Clustering Models 232

11.4 Analyses of Residuals on Fuzzy Regression Clustering Models 237

11.5 Numerical Examples 242

11.6 Conclusion 245

References 245

12 Implementing Hierarchical Fuzzy Clustering in Fuzzy Modeling Using the Weighted Fuzzy C-means 247
George E. Tsekouras

12.1 Introduction 247

12.2 Takagi and Sugeno’s Fuzzy Model 248

12.3 Hierarchical Clustering-based Fuzzy Modeling 249

12.4 Simulation Studies 256

12.5 Conclusions 261

References 261

13 Fuzzy Clustering Based on Dissimilarity Relations Extracted from Data 265
Mario G.C.A. Cimino, Beatrice Lazzerini and Francesco Marcelloni

13.1 Introduction 265

13.2 Dissimilarity Modeling 267

13.3 Relational Clustering 275

13.4 Experimental Results 280

13.5 Conclusions 281

References 281

14 Simultaneous Clustering and Feature Discrimination with Applications 285
Hichem Frigui

14.1 Introduction 285

14.2 Background 287

14.3 Simultaneous Clustering and Attribute Discrimination (SCAD) 289

14.4 Clustering and Subset Feature Weighting 296

14.5 Case of Unknown Number of Clusters 298

14.6 Application 1: Color Image Segmentation 298

14.7 Application 2: Text Document Categorization and Annotation 302

14.8 Application 3: Building a Multi-modal Thesaurus from Annotated Images 305

14.9 Conclusions 309

Appendix 14A.1 310

Acknowledgements 311

References 311

Part IV Real-time and Dynamic Clustering 313

15 Fuzzy Clustering in Dynamic Data Mining – Techniques and Applications 315
Richard Weber

15.1 Introduction 315

15.2 Review of Literature Related to Dynamic Clustering 315

15.3 Recent Approaches for Dynamic Fuzzy Clustering 317

15.4 Applications 324

15.5 Future Perspectives and Conclusions 331

Acknowledgement 331

References 331

16 Fuzzy Clustering of Parallel Data Streams 333
Jürgen Beringer and Eyke Hüllermeier

16.1 Introduction 333

16.2 Background 334

16.3 Preprocessing and Maintaining Data Streams 336

16.4 Fuzzy Clustering of Data Streams 340

16.5 Quality Measures 343

16.6 Experimental Validation 345

16.7 Conclusions 350

References 351

17 Algorithms for Real-time Clustering and Generation of Rules from Data 353
Dimitar Filev and Plamer Angelov

17.1 Introduction 353

17.2 Density-based Real-time Clustering 355

17.3 FSPC: Real-time Learning of Simplified Mamdani Models 358

17.4 Applications 362

17.5 Conclusion 367

References 368

Part V Applications and Case Studies 371

18 Robust Exploratory Analysis of Magnetic Resonance Images using FCM with Feature Partitions 373
Mark D. Alexiuk and Nick J. Pizzi

18.1 Introduction 373

18.2 FCM with Feature Partitions 374

18.3 Magnetic Resonance Imaging 379

18.4 FMRI Analysis with FCMP 381

18.5 Data-sets 382

18.6 Results and Discussion 384

18.7 Conclusion 390

Acknowledgements 390

References 390

19 Concept Induction via Fuzzy C-means Clustering in a High-dimensional Semantic Space 393
Dawei Song, Guihong Cao, Peter Bruza and Raymond Lau

19.1 Introduction 393

19.2 Constructing a High-dimensional Semantic Space via Hyperspace Analogue to Language 395

19.3 Fuzzy C-means Clustering 397

19.4 Word Clustering on a HAL Space – A Case Study 399

19.5 Conclusions and Future Work 402

Acknowledgement 402

References 402

20 Novel Developments in Fuzzy Clustering for the Classification of Cancerous Cells using FTIR Spectroscopy 405
Xiao-Ying Wang, Jonathan M. Garibaldi, Benjamin Bird and Mike W. George

20.1 Introduction 405

20.2 Clustering Techniques 406

20.3 Cluster Validity 412

20.4 Simulated Annealing Fuzzy Clustering Algorithm 413

20.5 Automatic Cluster Merging Method 418

20.6 Conclusion 423

Acknowledgements 424

References 424

Index 427