List of Contributors xi
Foreword xv
Preface xvii
Part I Fundamentals 1
1 Fundamentals of Fuzzy Clustering 3
Rudolf Kruse, Christian Doring 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
Janos Abonyi and Balazs 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
Jurgen Beringer and Eyke Hullermeier
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
