Advances in Fuzzy Clustering and its Applications

José Valente de Oliveira received his Ph.D. (1996), M.Sc. (1992), and the “Licenciado” degree in Electrical and Computer Engineering from the IST, Technical University of Lisbon.  Currently he is an Assistant Professor in the Faculty of Science and Technology at the University of Algarve where he served as Deputy Dean from 2002-2003.  He was recently appointed director of the University of Algarve Informatics Lab, a research laboratory specializing in computational intelligence including fuzzy sets, fuzzy and intelligent systems, machine learning, and optimization. Witold Pedrycz is a Professor and Canada Research Chair (CRC) in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada.  He is also with the Systems Research Institute of the Polish Academy of Sciences.  He is actively pursuing research in computational intelligence, fuzzy modeling, knowledge discovery and data mining, fuzzy control including fuzzy controllers, pattern recognition, knowledge-based neural networks, relational computation, bioinformatics, and Software Engineering.  He currently serves as an Associate Editor of IEEE Transactions on Fuzzy Systems.

Researchers, as well as those with incipient interest in the field, will find this book very useful and informative. (Computing Reviews, July 8, 2008)

• List of Contributors xiForeword xvPreface xviiPart I Fundamentals 11 Fundamentals of Fuzzy Clustering 3Rudolf Kruse, Christian Döring and Marie-Jeanne Lesot1.1 Introduction 31.2 Basic Clustering Algorithms 41.3 Distance Function Variants 141.4 Objective Function Variants 181.5 Update Equation Variants: Alternating Cluster Estimation 251.6 Concluding Remarks 27Acknowledgements 28References 292 Relational Fuzzy Clustering 31Thomas A. Runkler2.1 Introduction 312.2 Object and Relational Data 312.3 Object Data Clustering Models 342.4 Relational Clustering 382.5 Relational Clustering with Non-spherical Prototypes 412.6 Relational Data Interpreted as Object Data 452.7 Summary 462.8 Experiments 462.9 Conclusions 49References 503 Fuzzy Clustering with Minkowski Distance Functions 53Patrick J.F. Groenen, Uzay Kaymak and Joost van Rosmalen3.1 Introduction 533.2 Formalization 543.3 The Majorizing Algorithm for Fuzzy C-means with Minkowski Distances 563.4 The Effects of the Robustness Parameter l 603.5 Internet Attitudes 623.6 Conclusions 65References 664 Soft Cluster Ensembles 69Kunal Punera and Joydeep Ghosh4.1 Introduction 694.2 Cluster Ensembles 714.3 Soft Cluster Ensembles 754.4 Experimental Setup 784.5 Soft vs. Hard Cluster Ensembles 824.6 Conclusions and Future Work 90Acknowledgements 90References 90Part II Visualization 935 Aggregation and Visualization of Fuzzy Clusters Based on Fuzzy Similarity Measures 95János Abonyi and Balázs Feil5.1 Problem Definition 975.2 Classical Methods for Cluster Validity and Merging 995.3 Similarity of Fuzzy Clusters 1005.4 Visualization of Clustering Results 1035.5 Conclusions 116Appendix 5A.1 Validity Indices 117Appendix 5A.2 The Modified Sammon Mapping Algorithm 120Acknowledgements 120References 1206 Interactive Exploration of Fuzzy Clusters 123Bernd Wiswedel, David E. Patterson and Michael R. Berthold6.1 Introduction 1236.2 Neighborgram Clustering 1256.3 Interactive Exploration 1316.4 Parallel Universes 1356.5 Discussion 136References 136Part III Algorithms and Computational Aspects 1377 Fuzzy Clustering with Participatory Learning and Applications 139Leila Roling Scariot da Silva, Fernando Gomide and Ronald Yager7.1 Introduction 1397.2 Participatory Learning 1407.3 Participatory Learning in Fuzzy Clustering 1427.4 Experimental Results 1457.5 Applications 1487.6 Conclusions 152Acknowledgements 152References 1528 Fuzzy Clustering of Fuzzy Data 155Pierpaolo D’Urso8.1 Introduction 1558.2 Informational Paradigm, Fuzziness and Complexity in Clustering Processes 1568.3 Fuzzy Data 1608.4 Fuzzy Clustering of Fuzzy Data 1658.5 An Extension: Fuzzy Clustering Models for Fuzzy Data Time Arrays 1768.6 Applicative Examples 1808.7 Concluding Remarks and Future Perspectives 187References 1899 Inclusion-based Fuzzy Clustering 193Samia Nefti-Meziani and Mourad Oussalah9.1 Introduction 1939.2 Background: Fuzzy Clustering 1959.3 Construction of an Inclusion Index 1969.4 Inclusion-based Fuzzy Clustering 1989.5 Numerical Examples and Illustrations 2019.6 Conclusions 206Acknowledgements 206Appendix 9A.1 207References 20810 Mining Diagnostic Rules Using Fuzzy Clustering 211Giovanna Castellano, Anna M. Fanelli and Corrado Mencar10.1 Introduction 21110.2 Fuzzy Medical Diagnosis 21210.3 Interpretability in Fuzzy Medical Diagnosis 21310.4 A Framework for Mining Interpretable Diagnostic Rules 21610.5 An Illustrative Example 22110.6 Concluding Remarks 226References 22611 Fuzzy Regression Clustering 229Mikal Sato-Ilic11.1 Introduction 22911.2 Statistical Weighted Regression Models 23011.3 Fuzzy Regression Clustering Models 23211.4 Analyses of Residuals on Fuzzy Regression Clustering Models 23711.5 Numerical Examples 24211.6 Conclusion 245References 24512 Implementing Hierarchical Fuzzy Clustering in Fuzzy Modeling Using the Weighted Fuzzy C-means 247George E. Tsekouras12.1 Introduction 24712.2 Takagi and Sugeno’s Fuzzy Model 24812.3 Hierarchical Clustering-based Fuzzy Modeling 24912.4 Simulation Studies 25612.5 Conclusions 261References 26113 Fuzzy Clustering Based on Dissimilarity Relations Extracted from Data 265Mario G.C.A. Cimino, Beatrice Lazzerini and Francesco Marcelloni13.1 Introduction 26513.2 Dissimilarity Modeling 26713.3 Relational Clustering 27513.4 Experimental Results 28013.5 Conclusions 281References 28114 Simultaneous Clustering and Feature Discrimination with Applications 285Hichem Frigui14.1 Introduction 28514.2 Background 28714.3 Simultaneous Clustering and Attribute Discrimination (SCAD) 28914.4 Clustering and Subset Feature Weighting 29614.5 Case of Unknown Number of Clusters 29814.6 Application 1: Color Image Segmentation 29814.7 Application 2: Text Document Categorization and Annotation 30214.8 Application 3: Building a Multi-modal Thesaurus from Annotated Images 30514.9 Conclusions 309Appendix 14A.1 310Acknowledgements 311References 311Part IV Real-time and Dynamic Clustering 31315 Fuzzy Clustering in Dynamic Data Mining – Techniques and Applications 315Richard Weber15.1 Introduction 31515.2 Review of Literature Related to Dynamic Clustering 31515.3 Recent Approaches for Dynamic Fuzzy Clustering 31715.4 Applications 32415.5 Future Perspectives and Conclusions 331Acknowledgement 331References 33116 Fuzzy Clustering of Parallel Data Streams 333Jürgen Beringer and Eyke Hüllermeier16.1 Introduction 33316.2 Background 33416.3 Preprocessing and Maintaining Data Streams 33616.4 Fuzzy Clustering of Data Streams 34016.5 Quality Measures 34316.6 Experimental Validation 34516.7 Conclusions 350References 35117 Algorithms for Real-time Clustering and Generation of Rules from Data 353Dimitar Filev and Plamer Angelov17.1 Introduction 35317.2 Density-based Real-time Clustering 35517.3 FSPC: Real-time Learning of Simplified Mamdani Models 35817.4 Applications 36217.5 Conclusion 367References 368Part V Applications and Case Studies 37118 Robust Exploratory Analysis of Magnetic Resonance Images using FCM with Feature Partitions 373Mark D. Alexiuk and Nick J. Pizzi18.1 Introduction 37318.2 FCM with Feature Partitions 37418.3 Magnetic Resonance Imaging 37918.4 FMRI Analysis with FCMP 38118.5 Data-sets 38218.6 Results and Discussion 38418.7 Conclusion 390Acknowledgements 390References 39019 Concept Induction via Fuzzy C-means Clustering in a High-dimensional Semantic Space 393Dawei Song, Guihong Cao, Peter Bruza and Raymond Lau19.1 Introduction 39319.2 Constructing a High-dimensional Semantic Space via Hyperspace Analogue to Language 39519.3 Fuzzy C-means Clustering 39719.4 Word Clustering on a HAL Space – A Case Study 39919.5 Conclusions and Future Work 402Acknowledgement 402References 40220 Novel Developments in Fuzzy Clustering for the Classification of Cancerous Cells using FTIR Spectroscopy 405Xiao-Ying Wang, Jonathan M. Garibaldi, Benjamin Bird and Mike W. George20.1 Introduction 40520.2 Clustering Techniques 40620.3 Cluster Validity 41220.4 Simulated Annealing Fuzzy Clustering Algorithm 41320.5 Automatic Cluster Merging Method 41820.6 Conclusion 423Acknowledgements 424References 424Index 427