## Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image RecognitionFuzzy Cluster Analysis presents advanced and powerful fuzzy clustering techniques. This thorough and self-contained introduction to fuzzy clustering methods and applications covers classification, image recognition, data analysis and rule generation. Combining theoretical and practical perspectives, each method is analysed in detail and fully illustrated with examples. Features include: * Sections on inducing fuzzy if-then rules by fuzzy clustering and non-alternating optimization fuzzy clustering algorithms * Discussion of solid fuzzy clustering techniques like the fuzzy c-means, the Gustafson-Kessel and the Gath-and-Geva algorithm for classification problems * Focus on linear and shell clustering techniques used for detecting contours in image analysis * Accompanying software and data sets pertaining to the examples presented, enabling the reader to learn through experimentation * Examination of the difficulties involved in evaluating the results of fuzzy cluster analysis and of determining the number of clusters with analysis of global and local validity measures * Description of different fuzzy clustering techniques allowing the user to select the method most appropriate to a particular problem Computer scientists, engineers and mathematicians in industry and research who are concerned with fuzzy clustering methods, data analysis, pattern recognition or image processing will find this a timely and accessible resource. Graduate students in computer science, mathematics or statistics will value this comprehensive overview of the applications of fuzzy methods. Download accompanying program and data sets from our website |

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### Contents

Basic Concepts | 5 |

Classical Fuzzy Clustering Algorithms | 35 |

Linear and Ellipsoidal Prototypes | 61 |

Shell Prototypes | 77 |

Polygonal Object Boundaries | 115 |

Cluster Estimation Models | 157 |

Cluster Validity | 185 |

Rule Generation with Clustering | 239 |

Appendix | 271 |

277 | |

286 | |

### Common terms and phrases

AFCS analysis Figure analysis space applied approximation assigned chapter classification clus cluster analysis cluster centres cluster number cluster shapes clustering result cmax computed contour density convergence covariance matrix crisp data analysis data set data vectors datum defined defuzzification detection determined distance function edge detection edge lengths eigenvalue eigenvectors ellipses equations Euclidean distance Euclidean norm example FC2RS FCES FCM-AO FCQS FCRS FCSS fuzzifier fuzzy c-means algorithm fuzzy clustering fuzzy sets Gath-Geva algorithm Gustafson-Kessel algorithm high memberships hyperbolas hyperconic initialization input space intuitive partition iteration steps linear clusters local minima maximum membership degrees membership functions merged MFCQS minimized minimum functions noise cluster noise data number of clusters number of data objective function obtain optimization parameters pixels positive definite possibilistic clustering probabilistic cluster partition problem prototypes quadric recognized rectangle respect set from figure shell clustering shown in figure straight line segments theorem UFCSS algorithm validity measures values zero

### References to this book

Fuzzy Decision Making in Modeling and Control João M. C. Sousa,Uzay Kaymak No preview available - 2002 |

Computational Intelligence in Software Quality Assurance Scott Dick,Abraham Kandel Limited preview - 2005 |