模糊聚类分析--分类,数据分析与图像识别方法(英文版)

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Fuzzy Cluster Analysis -Methods for Classification,Data Analysis and Image Recognition Frank Hoppner, Frank Klawonn, Rudolf Kruse,Thomas Runkler 著 目录 1 Basic Concepts 1.1 Analysis of data 1.2 Cluster analysis 1.3 Objective functilm-based cluster analysis 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 sl}ells 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 Ptototype defuzzification. 6.5 ACE for higher-order prototypes 6.6 Acceleration of the Clustering Process 6.6.1 Fast Alternating Cluster Estimation (F.-\CE) 6.6.2 Regular Alternating Cluster Estimation (rACE) 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 T
Contents Preface X Introduction 1 Basic Concepts 1.1 Analysis of data 1.2 Cluster analysis 8 1.3 Obiective function-based cluster analysis 11 1.4 Fuzzy analysis of data 17 1.5 Special objective functions 20 1. 6 A principal clustering algorithm 28 1.7 Unknown number of clusters problem 31 2 Classical Fuzzy Clustering Algorithms 35 2.1 The fuzzy c-means algorithm 37 2.2 The Gustafson-Kessel algorithm 43 2.3 The Gath-Geva algorithm 49 2.4 Simplified versions of GK and GG 54 2.5 Computational effort 58 3 Linear and Ellipsoidal Prototypes 61 3. 1 The fuzzy c-varieties algorithm 61 3.2 The adaptive fuzzy clustering algorithm 70 3.3 Algorithms by Gustafson/Kessel and Gath/Geva 74 3.4 Computational effort 75 4 Shell Prototypes 77 4.1 The fuzzy c-shells algorithm 78 4.2 The fuzzy c-spherical shells algorithm 83 4.3 The adaptive fuzzy. c-shells algorithm 86 CONTENTS 4.4 The fuzzy c-ellipsoidal shells algorithm 92 4.5 The fuzzy c-ellipses algorithm 99 4.6 The fuzzy c-quadric shells algorithm .101 4.7 The modified FCQSs algorithm 107 4.8 Computational effort 113 5 Polygonal Object Boundaries 115 5.1 Detection of rectangles 117 5.2 The fuzzy c-rectangular shells algorithm 132 5.3 The fuzzy c-2-rectangular shells algorithm 145 5.4 Computational effort ,,,,,,155 6 Cluster Estimation Models 157 6.1 AO membership functions 158 6.2 ACE membership functions .159 6.3 Hyperconic clustering(dancing cones) 161 6.4 Pfototype defuzzification 165 6.5 ACE for higher-order prototypes 171 6.6 Acceleration of the Clustering Process 177 6.6.1 Fast Alternating Cluster Estimation(FACE) 178 6.6.2 Regular Alternating Cluster Estimation (rACE).. 182 6.7 Comparison: AO and ACE 183 7 Cluster Validity 185 7. 1 Global validity measures 188 7.1.1 Solid clustering validity measures 188 7.1.2 Shell clustering validity measures 198 7. 2 Local validity measures 200 7.2.1 The compatible cluster merging algorithm 201 7.2.2 The unsupervised FCSS algorithm .....,... 207 7.2.3 The contour density criterion 215 7. 2. 4 The unsupervised (M)FCQS algorithm ,221 7.3 Initialization by edge detection ......... 233 8 Rule Generation with Clustering 239 8.1 From membership matrices to membership functions 239 8.1.1 Interpolation 240 8.1.2 Projection and cylindrical extension 241 8.1.3 Convex completion 243 8.1.4 Approximation 244 8.1.5 Cluster estimation with ACE 247 CONTENTS 8.2 Rules for fuzzy classifiers ...248 8.2. 1 Input space clustering 249 8.2.2 Cluster projection 250 8.2.3 Input output product space clustering 261 8.3 Rules for function approximation 261 8.3.1 Input ouput product space clustering....,...261 8.3.2 Input space clustering 266 8.3.3 Output space clusterin 1g 268 8.4 Choice of the clustering domain 268 Appendix 271 AI Notation 271 A2 Influence of scaling on the cluster partition 271 A3 Overview on FCQS cluster shapes .274 A4 Transformation to straight lines 274 References 277 Index 286 Preface When Lotfi Zadeh introduced the notion of a"fuzzy set"in 1965, his mary objective was to set up a formal framework for the representation and management of vague and uncertain knowledge. More than 20 years passed until fuzzy systems became established in industrial applicationis to a larger extent. Today, they are routinely applied especially in the field of control engineering. As a result of their success to translate knowledge-based ap proaches into a formal model that is also easy to implement, a great variety of methods for the usage of fuzzy techniques has been developed during the last years in the area of data analysis. Besides the possibility to take into account uncertainties within data, fuzzy data analysis allows us to learn a transparent, and knowledge-based representation of the information in- herent in the data. Areas of application for fuzzy cluster analysis include exploratory data analysis for pre-structuring data, classification and ap proximation problems, and the recognition of geometrical shapes in image processing 13kt)k|M必n图 When writing this book, our intention was to give a self-contained and methodical introduction to fuzzy cluster analysis with its areas of applica tion and to provide a systematic description of different fuzzy clustering techniques, from which the user can choose the methods appropriate for his problem. The book applies to computer scientists, engineers and math ematicians in industry, research and teaching, who are occupied with data analysis, pattern recognition or image processing, or who take into consid eration the application of fuzzy clustering methods in their area of work Some basic knowledge in linear algebra is presupposed for the comprehen sion of the techniques and especially their derivation. Familiarity with fuzzy systems is not a requirement, because only in the chapter on rule generation with fuzzy clustering, more than the notion of a"fuzzy set "is necessary for understanding, and in addition, the basics of fuzzy systems are provided in that chapter. Although this title is presented as a text book we have not included exercises for students, since it would not make sense to carry out the al- X PREFACE gorithms by hand: We think that applying the algorithms to example data sets is the appropriate way to get a better understanding of the tech niques. A software tool implementing most of th e algorithms presented in chapters 1-5 and 7 together with the many example data sets discussed in this book are available as public domain software via the Internet at http://fuzzy.cs.uni-magdeburg.de/clusterbook/ The book is an extension of a translation of our German book on fuzzy cluster analysis published by Vieweg Verlag in 1997. Most parts of the translation were carried out by Mark-Andre Krogel. The book would prob. ably have appeared years later without his valuable support. The material of the book is partly based on lectures on fuzzy systems, fuzzy data analysis and fuzzy control that we gave at the Technical University of Braunschweig at the University“ Otto von guericke” Magdeburg, at the University“Jo hannes Kepler"Linz, and at Ostfriesland University of Applied Sciences in Emden. The book is also based on a project in the framework of a research bar contract with Fraunhofer-Gesellschaft, on results from several industrial projects at Siemens Corporate Technology(Munich), and on joint work with Jim Bezdek at the University of West Florida. We thank Wilfried ,aev Euing and Hartmut Wolf for their advisory support during this project We would also like to express our thanks for the great support to Juliet Booker, Rhoswen Cowell, Peter Mitchell from Wiley and Reinald Klocken busch from our German publisher Vieweg Verlag. Frank Hoppner Frank Klawonn Rudolf Kruse Thomas Runkler Introduction - ips.-E,k For a fraction of a second, the receptors are fed with half a million items of data. Without any measurable time delay, those data items are evaluated and analysed, and their essential contents are recognized parallE A glance at an image from TV or a newspaper, human beings are capable aE,lwityof this technically complex performance, which has not yet been achieved by ti(to) any computer with comparable results. The bottleneck is no longer the op- tical sensors or data transmission, but the analysis and extraction of essen rS. tial information. A single glance is sufficient for humans to identify circles and straight lines in accumulations of points and to produce an assignment between objects and points in the picture. Those points cannot always he assigned unambiguously to picture objects, although that hardly impairs human recognition performance. However, it is a big problem to model this decision with the help of an algorithm. The demand for an automatic anal- ysis is high, though. Be it for the development of an autopilot for vehicle control, for visual quality control or for comparisons of large amounts of image data. The problem with the development of such a procedure is that humans cannot verbally reproduce their own procedures for image recogni- tion, because it happens unconsciously. Conversely, humans have consider able difficulties recognizing relations in multi-dimensional data records that cannot be graphically represented. Here, they are dependent on computer supported techniques for data analysis, for which it is irrelevant whether the data consists of two- or twelve-dimensional vectors The introduction of fuzzy sets by L A. Zadeh [104] in 1965 defined an object that allows the mathematical modelling of imprecise propositions Since then this method has been employed in many areas to simulate how inferences are made by humans, or to manage uncertain information. This method can also be applied to data and image analysis Cluster analysis deals with the discovery of structures or groupings within data. Since hardly ever any disturbance or noise can be completely eliminated, some inherent data uncertainty cannot be avoided. That is INTRODUCTION why fuzzy cluster analysis dispenses with unambiguous mapping of the data to classes and clusters, and instead computes degrees of membership Chat specify to what extend data belong to clusters The introductory chapter 1 relates fuzzy cluster analysis to the more general areas of cluster and data analysis, and provides the basic terminal ogy. Here we focus on objective function models whose aim is to assign the data to clusters so that a given objective function is optimized. The objective function assigns a quality or error to each cluster arrangement based on the distance between the data and the typical representatives of the clusters. We show how the objective function models can be optimized using an alternating optimization algorithm. Chapter 2 is dedicated to fuzzy cluster analysis algorithms for the recog nition of point-like clusters of different size and shape, which play a central role in data analysis The linear clustering techniques described in chapter 3 are suitable for the detection of clusters formed like straight lines, planes or hyperplanes because of the suitable modification of the distance function that occurs in the objective functions. These techniques are appropriate for image processing, as well as for the construction of locally linear models of data with underlying functional interrelations Chapter 4 introduces shell clustering techniques, that aim to recog nize geometrical contours such as borders of circles and ellipses by further modifications of the distance function. An extension of these techniques to non-smooth structures such as rectangles or other polygons is given in chapter 5. The cluster estimation models described in chapter 6 abandon the ob- jective function model. This allows handling of complex or not explicitl accessible systems, and leads to a generalized model with user-defined mem bership functions and prototypes Besides the assignment of data to classes, the determination of the num ber of clusters is a central problem in data analysis, which is also related to the more general problem of cluster validity. The aim of cluster valid ity is to evaluate whether clusters determined in an analysis are relevant or meaningful, or whether there might be no structure in the data that is covered by the clustering model. Chapter 7 provides an overview on cluster validity, and concentrates mainly on methods to determine the number of clusters, which are tailored to the different clustering algorithms Clusters can be interpreted as if-then rules. The structure information discovered by fuzzy clustering can therefore be translated to human read able fuzzy rule bases. The necessary techniques for this rule extraction are presented in chapter 8 INTRODUCTION 3 Readers who are interested in watching the algorithms at work candownloadfreesoftwareviatheInternetfromhttp://fuzzy.cs.uni- magdeburg.de/clusterbook/

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cogemm 看的不清楚 有点小郁闷 不过还是谢谢楼主分享
2014-07-01
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amengi 这一领域比较经典的书,只是不是很清晰
2013-03-25
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adorare 对传统方法总结比较充分,不过方法有点老了。打个基础。
2012-07-12
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