Description
Frank Höppner, Frank Klawonn, Rudolf Kruse and Thomas
Runkler: Fuzzy Cluster Analysis, Wiley (1999)
(ISBN
0-471-98864-2, 289 pp, £ 45.00)
Fuzzy 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.
- 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
- 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
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Table of Contents
Introduction
1 Basic Concepts
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
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
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
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 algorithm
4.6 The fuzzy c-quadric shells algorithm
4.7 The modified FCQS algorithm
4.8 Computational effort
5 Polygonal Object Boundaries
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
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
6.6.2 Regular Alternating Cluster Estimation
6.7 Comparison: AO and ACE
7 Cluster Validity
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
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
8.2 Rules for fuzzy classifiers
8.2.1 Input space clustering
8.2.2 Cluster projection
8.2.3 Input output product space clustering
8.3 Rules 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
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
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