Advances in Fuzzy Clustering and its Applications

A comprehensive, coherent, and in depth presentation of the state of the art in fuzzy clustering. Fuzzy clustering is now a mature and vibrant area of research with highly innovative advanced applications. Encapsulating this through presenting a careful selection of research contributions, this book addresses timely and relevant concepts and methods, whilst identifying major challenges and recent developments in the area. Split into five clear sections, Fundamentals, Visualization, Algorithms and Computational Aspects, Real-Time and Dynamic Clustering, and Applications and Case Studies, the book covers a wealth of novel, original and fully updated material, and in particular offers: a focus on the algorithmic and computational augmentations of fuzzy clustering and its effectiveness in handling high dimensional problems, distributed problem solving and uncertainty management. presentations of the important and relevant phases of cluster design, including the role of information granules, fuzzy sets in the realization of human-centricity facet of data analysis, as well as system modelling demonstrations of how the results facilitate further detailed development of models, and enhance interpretation aspects a carefully organized illustrative series of applications and case studies in which fuzzy clustering plays a pivotal role This book will be of key interest to engineers associated with fuzzy control, bioinformatics, data mining, image processing, and pattern recognition, while computer engineers, students and researchers, in most engineering disciplines, will find this an invaluable resource and research tool.

Table of Contents:
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