Knowledge-Based Clustering From Data to Information Granules

by Pedrycz, Witold

• ISBN13: 9780471469667
• ISBN10: 0471469661
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-01-28
• Publisher: Wiley-Interscience

Summary

A comprehensive coverage of emerging and current technology dealing with heterogeneous sources of information, including data, design hints, reinforcement signals from external datasets, and related topics Covers all necessary prerequisites, and if necessary,additional explanations of more advanced topics, to make abstract concepts more tangible Includes illustrative material andwell-known experimentsto offer hands-on experience

Author Biography

WITOLD PEDRYCZ, PHD, is a Professor and Canada Research Chair at the University of Alberta, Canada. He is also with the Systems Research Institute of The Polish Academy of Sciences, Warsaw, Poland. Dr. Pedrycz is a Fellow of the IEEE, has authored nine research monographs, edited six volumes, and has written numerous papers in computational intelligence, granular computing, pattern recognition, quantitative software engineering, and data mining.

Table of Contents

Foreword	xiii
Preface	xv
1 Clustering and Fuzzy Clustering	1	(27)
1.1 Introduction	1	(1)
1.2 Basic Notions and Notation	1	(5)
1.2.1 Types of Data	2	(1)
1.2.2 Distance and Similarity	2	(4)
1.3 Main Categories of Clustering Algorithms	6	(4)
1.3.1 Hierarchical Clustering	6	(2)
1.3.2 Objective Function-Based Clustering	8	(2)
1.4 Clustering and Classification	10	(1)
1.5 Fuzzy Clustering	11	(7)
1.6 Cluster Validity	18	(1)
1.7 Extensions of Objective Function-Based Fuzzy Clustering	19	(4)
1.7.1 Augmented Geometry of Fuzzy Clusters: Fuzzy C Varieties	19	(1)
1.7.2 Possibilistic Clustering	20	(2)
1.7.3 Noise Clustering	22	(1)
1.8 Self-Organizing Maps and Fuzzy Objective Function-Based Clustering	23	(2)
1.9 Conclusions	25	(1)
References	26	(2)
2 Computing with Granular Information: Fuzzy Sets and Fuzzy Relations	28	(22)
2.1 A Paradigm of Granular Computing: Information Granules and Their Processing	28	(3)
2.2 Fuzzy Sets as Human-Centric Information Granules	31	(1)
2.3 Operations on Fuzzy Sets	32	(1)
2.4 Fuzzy Relations	33	(2)
2.5 Comparison of Two Fuzzy Sets	35	(2)
2.6 Generalizations of Fuzzy Sets	37	(1)
2.7 Shadowed Sets	38	(6)
2.8 Rough Sets	44	(2)
2.9 Granular Computing and Distributed Processing	46	(1)
2.10 Conclusions	47	(1)
References	47	(3)
3 Logic-Oriented Neurocomputing	50	(16)
3.1 Introduction	50	(1)
3.2 Main Categories of Fuzzy Neurons	51	(8)
3.2.1 Aggregative Neurons	52	(3)
3.2.2 Referential (Reference) Neurons	55	(4)
3.3 Architectures of Logic Networks	59	(2)
3.4 Interpretation Aspects of the Networks	61	(1)
3.5 Granular Interfaces of Logic Processing	62	(2)
3.6 Conclusions	64	(1)
References	64	(2)
4 Conditional Fuzzy Clustering	66	(21)
4.1 Introduction	66	(2)
4.2 Problem Statement: Context Fuzzy Sets and Objective Function	68	(2)
4.3 The Optimization Problem	70	(10)
4.4 Computational Considerations of Conditional Clustering	80	(1)
4.5 Generalizations of the Algorithm Through the Aggregation Operator	81	(1)
4.6 Fuzzy Clustering with Spatial Constraints	82	(4)
4.7 Conclusions	86	(1)
References	86	(1)
5 Clustering with Partial Supervision	87	(10)
5.1 Introduction	87	(1)
5.2 Problem Formulation	88	(2)
5.3 Design of the Clusters	90	(1)
5.4 Experimental Examples	91	(2)
5.5 Cluster-Based Tracking Problem	93	(3)
5.6 Conclusions	96	(1)
References	96	(1)
6 Principles of Knowledge-Based Guidance in Fuzzy Clustering	97	(32)
6.1 Introduction	97	(2)
6.2 Examples of Knowledge-Oriented Hints and Their General Taxonomy	99	(3)
6.3 The Optimization Environment of Knowledge-Enhanced Clustering	102	(3)
6.4 Quantification of Knowledge-Based Guidance Hints and Their Optimization	105	(2)
6.5 Organization of the Interaction Process	107	(5)
6.6 Proximity-Based Clustering (P-FCM)	112	(5)
6.7 Web Exploration and P-FCM	117	(9)
6.8 Linguistic Augmentation of Knowledge-Based Hints	126	(1)
6.9 Conclusions	127	(1)
References	127	(2)
7 Collaborative Clustering	129	(29)
7.1 Introduction and Rationale	129	(2)
7.2 Horizontal and Vertical Clustering	131	(1)
7.3 Horizontal Collaborative Clustering	132	(8)
7.3.1 Optimization Details	135	(2)
7.3.2 The Flow of Computing of Collaborative Clustering	137	(1)
7.3.3 Quantification of the Collaborative Phenomenon of Clustering	138	(2)
7.4 Experimental Studies	140	(10)
7.5 Further Enhancements of Horizontal Clustering	150	(1)
7.6 The Algorithm of Vertical Clustering	151	(2)
7.7 A Grid Model of Horizontal and Vertical Clustering	153	(2)
7.8 Consensus Clustering	155	(2)
7.9 Conclusions	157	(1)
References	157	(1)
8 Directional Clustering	158	(20)
8.1 Introduction	158	(1)
8.2 Problem Formulation	159	(4)
8.2.1 The Objective Function	160	(1)
8.2.2 The Logic Transformation Between Information Granules	161	(2)
8.3 The Algorithm	163	(3)
8.4 The Development Framework of Directional Clustering	166	(1)
8.5 Numerical Studies	167	(7)
8.6 Conclusions	174	(2)
References	176	(2)
9 Fuzzy Relational Clustering	178	(13)
9.1 Introduction and Problem Statement	178	(1)
9.2 FCM for Relational Data	179	(2)
9.3 Decomposition of Fuzzy Relational Patterns	181	(7)
9.3.1 Gradient-Based Solution to the Decomposition Problem	182	(2)
9.3.2 Neural Network Model of the Decomposition Problem	184	(4)
9.4 Comparative Analysis	188	(1)
9.5 Conclusions	189	(1)
References	189	(2)
10 Fuzzy Clustering of Heterogeneous Patterns	191	(18)
10.1 Introduction	191	(1)
10.2 Heterogeneous Data	192	(2)
10.3 Parametric Models of Granular Data	194	(1)
10.4 Parametric Mode of Heterogeneous Fuzzy Clustering	195	(3)
10.5 Nonparametric Heterogeneous Clustering	198	(9)
10.5.1 A Frame of Reference	198	(2)
10.5.2 Representation of Granular Data Through the Possibility-Necessity Transformation	200	(5)
10.5.3 Dereferencing	205	(2)
10.6 Conclusions	207	(1)
References	208	(1)
11 Hyperbox Models of Granular Data: The Tchebyschev FCM	209	(17)
11.1 Introduction	209	(1)
11.2 Problem Formulation	210	(1)
11.3 The Clustering Algorithm Detailed Considerations	211	(7)
11.4 Development of Granular Prototypes	218	(2)
11.5 Geometry of Information Granules	220	(3)
11.6 Granular Data Description: A General Model	223	(1)
11.7 Conclusions	223	(1)
References	224	(2)
12 Genetic Tolerance Fuzzy Neural Networks	226	(20)
12.1 Introduction	226	(1)
12.2 Operations of Thresholding and Tolerance: Fuzzy Logic-Based Generalizations	227	(4)
12.3 Topology of the Logic Network	231	(4)
12.4 Genetic Optimization	235	(1)
12.5 Illustrative Numeric Studies	236	(8)
12.6 Conclusions	244	(1)
References	245	(1)
13 Granular Prototyping	246	(24)
13.1 Introduction	246	(1)
13.2 Problem Formulation	247	(4)
13.2.1 Expressing Similarity Between Two Fuzzy Sets	247	(1)
13.2.2 Performance Index (Objective Function)	248	(3)
13.3 Prototype Optimization	251	(12)
13.4 Development of Granular Prototypes	263	(5)
13.4.1 Optimization of the Similarity Levels	263	(1)
13.4.2 An Inverse Similarity Problem	264	(4)
13.5 Conclusions	268	(1)
References	268	(2)
14 Granular Mappings	270	(13)
14.1 Introduction and Problem Statement	270	(1)
14.2 Possibility and Necessity Measures as the Computational Vehicles of Granular Representation	271	(1)
14.3 Building the Granular Mapping	272	(3)
14.4 Designing Multivariable Granular Mappings Through Fuzzy Clustering	275	(3)
14.5 Quantification of Granular Mappings	278	(1)
14.6 Experimental Studies	278	(2)
14.7 Conclusions	280	(2)
References	282	(1)
15 Linguistic Modeling	283	(14)
15.1 Introduction	283	(2)
15.2 Cluster-Based Representation of Input-Output Mapping	285	(2)
15.3 Conditional Clustering in the Development of a Blueprint of Granular Models	287	(3)
15.4 The Granular Neuron as a Generic Processing Element in Granular Networks	290	(3)
15.5 The Architecture of Linguistic Models Based on Conditional Fuzzy Clustering	293	(1)
15.6 Refinements of Linguistic Models	294	(1)
15.7 Conclusions	295	(1)
References	296	(1)
Bibliography	297	(18)
Index	315