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Table of contents for Fuzzy cluster analysis : methods for classification, data analysis, and image recognition / Frank Höppner ... [et al.].




    Contents
    
      Preface                                  
      Introduction                             
  
    1 Basic Concepts      5                     
      1.1 Analysis of data                    
      1.2 Cluster analysis
      1.3 Objective function-based cluster analysis
      1.4 Fuzzy analysis of data 
      1.5 Special objective functions
      1.6 A principal clustering algorithm 
      1.7 Unknown number of clusters problem 
   
    2 Classical Fuzzy Clustering Algorithms    35
      2.1 The fuzzy c-means algorithm 
      2.2 The Gustafson-Kessel algorithm
      2.3 The Gath-Geva algorithm 
      2.4 Simplified versions of GK and GG
      2.5 Computational effort
   
    3 Linear and Ellipsoidal Prototypes        61
      3.1 The fuzzy c-varieties algorithm
      3.2 The adaptive fuzzy clustering algorithm 
      3.3 Algorithms by Gustafson/Kessel and Gath/Geva 
      3.4 Computational effort 
   
   4 Shell Prototypes                         77
      4.1 The fuzzy c-shells algorithm 
      4.2 The fuzzy c-spherical shells algorithm
      4.3 The adaptive fuzzy,c-shells algorithm 
      4.4 The fuzzy c-ellipsoidal shells algorithm
      4.5 The fuzzy c-ellipses algorithm9
      4.6 The fuzzy c-quadric shells algorithm
      4.7 The modified FCQS algorithm 
      4.8 Computational effort
    
   5 Polygonal Object Boundaries             115
      5.1 Detection of rectangles 
      5.2 The fuzzy c-rectangular shells algorithm 
      5.3 The fuzzy c-2-rectangular shells algorithm
      5.4 Computational effort
    
    6 Cluster Estimation Models               157
      6.1 AO membership functions 
      6.2 ACE membership functions
      6.3 Hyperconic clustering (dancing cones)
      6.4 Prototype defuzzification
      6.5 ACE for higher-order prototypes
      6.6 Acceleration of the Clustering Process
      6.6.1 Fast Alternating Cluster Estimation (FACE) 
      6.6.2 Regular Alternating Cluster Estimation (rACE)
      6.7 Comparison: AO and ACE
    
    7 Cluster Validity                        185
      7.1 Global validity measures 
      7.1.1 Solid clustering validity measures
      7.1.2 Shell clustering validity measures
      7.2 Local validity measures
      7.2.1 The compatible cluster merging algorithm
      7.2.2 The unsupervised FCSS algorithm 
      7.2.3 The contour density criterion
      7.2.4 The unsupervised (M)FCQS algorithm 
      7.3 Initialization by edge detection 
    
    8 Rule Generation with Clustering         239
      8.1 From membership matrices to
         membership functions 
       8.1.1 Interpolation 
       8.1.2 Projection and cylindrical extension
       8.1.3 Convex completion 
       8.1.4 Approximation
       8.1.5 Cluster estimation with ACE
       8.2Rules for fuzzy classifiers
       8.2.1 Input space clustering
       8.2.2 Cluster projection 
       8.2.3 Input output product space clustering
       8.3Rules for function approximation
       8.3.1 Input ouput product space clustering
       8.3.2 Input space clustering 
       8.3.3 Output space clustering 
       8.4 Choice of the clustering domain 
    
     Appendix                                 271
     A.1 Notation
     A.2 Influence of scaling on the cluster partition
     A.3 Overview on FCQS cluster shapes
     A.4 Transformation to straight lines
    
     References                               277
    
     Index                                   286