Advances in Fuzzy Clustering and its Applications

by Valente de Oliveira, Jose; Pedrycz, Witold

• ISBN13: 9780470027608
• ISBN10: 0470027606
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-06-05
• Publisher: WILEY

Summary

Divided into four sections the first section, 'Fuzzy clustering-the primer', covers the essentials of fuzzy clustering including motivation, basic algorithms, computing aspects, realisations, cluster validity assessment and ensuing interpretation of the results along with several representative areas of applications.  Chapters presenting the underlying fundamentals i.e. the 'Foundations' of fuzzy clustering follow this.  The authors elaborate on the role of fuzzy sets in data analysis, discuss the principles of data organization, present fundamental algorithms and their augmentations, identify pitfalls and embark on the interpretation issues.  Different paradigms of unsupervised learning along with so-called knowledge-based clustering and data organisation are also addressed.  The third section 'Algorithms and Computational Aspects' focuses on the algorithmic and computational augmentations of fuzzy clustering and demonstrates its effectiveness in highly dimensional problems, distributed problem solving and uncertainty handling.  To conclude the book, 'Applications and Case Studies' is devoted to a series of applications in which fuzzy clustering plays a pivotal role.  The primary intent is to discuss its role in the overall design process in various tasks of prediction, classification, control and modelling.  Here it becomes highly instructive to highlight at which phase of the design clustering is of relevance, what role it plays and how the results facilitate further detailed development of models or enhance interpretation aspects.

Author Biography

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.

Table of Contents

List of Contributors

Foreword

Preface

Fundamentals

Fundamentals of Fuzzy Clustering

Introduction

Basic Clustering Algorithms

Distance Function Variants

Objective Function Variants

Update Equation Variants: Alternating Cluster Estimation

Concluding Remarks

Acknowledgements

References

Relational Fuzzy Clustering

Introduction

Object and Relational Data

Object Data Clustering Models

Relational Clustering

Relational Clustering with Non-spherical Prototypes

Relational Data Interpreted as Object Data

Summary

Experiments

Conclusions

References

Fuzzy Clustering with Minkowski Distance Functions

Introduction

Formalization

The Majorizing Algorithm for Fuzzy C-means with Minkowski Distances

The Effects of the Robustness Parameter

Internet Attitudes

Conclusions

References

Soft Cluster Ensembles

Introduction

Cluster Ensembles

Soft Cluster Ensembles

Experimental Setup

Soft vs. Hard Cluster Ensembles

Conclusions and Future Work

Acknowledgements

References

Visualization

Aggregation and Visualization of Fuzzy Clusters Based on Fuzzy Similarity Measures

5.1

5.2

5.3

5.4

5.5

Validity Indices

The Modified Sammon Mapping Algorithm

Acknowledgements

References

Interactive Exploration of Fuzzy Clusters

Introduction

Neighborgram Clustering

Interactive Exploration

Parallel Universes

Discussion

References

Algorithms and Computational Aspects

Fuzzy Clustering with Participatory Learning and Applications

Introduction

Participatory Learning

Participatory Learning in Fuzzy Clustering

Experimental Results

Applications

Conclusions.Acknowledgements

References

Fuzzy Clustering of Fuzzy Data

Introduction

Informational Paradigm, Fuzziness and Complexity in Clustering Processes

Fuzzy Data

Fuzzy Clustering of Fuzzy Data

An Extension: Fuzzy Clustering Models for Fuzzy Data Time Arrays

Applicative Examples

Concluding Remarks and Future Perspectives

References

Inclusion-based Fuzzy Clustering

Introduction

Background: Fuzzy Clustering

Construction of an Inclusion Index

Inclusion-based Fuzzy Clustering

Numerical Examples and Illustrations

Conclusions

Acknowledgements

References

Mining Diagnostic Rules Using Fuzzy Clustering

Introduction

Fuzzy Medical Diagnosis

Interpretability in Fuzzy Medical Diagnosis

A Framework for Mining Interpretable Diagnostic Rules

An Illustrative Example

Concluding Remarks

References

Fuzzy Regression Clustering

Introduction

Statistical Weighted Regression Models

Fuzzy Regression Clustering Models

Analyses of Residuals on Fuzzy Regression Clustering Models

Numerical Examples

Conclusion

References

Implementing Hierarchical Fuzzy Clustering in Fuzzy Modeling Using the Weighted

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