Kaburlasos Towards a Unified Modeling and Knowledge-Representation based on Lattice Theory

Computational Intelligence and Soft Computing Applications
1. Auflage 2007
ISBN: 978-3-540-34170-3
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 27, 245 Seiten

Reihe: Studies in Computational Intelligence

This research monograph proposes a unified, cross-fertilizing approach for knowledge-representation and modeling based on lattice theory. The emphasis is on clustering, classification, and regression applications. It presents novel tools and useful perspectives for effective pattern classification. The material is multi-disciplinary based on on-going research published in major scientific journals and conferences.

Autoren/Hrsg.

Kaburlasos, Vassilis G.

Inhaltsverzeichnis

1;Foreword;6
2;Preface;8
3;Contents;10
4;Lists of Figures and Tables;14
5;Acronyms and Symbols;18
6;PART I: THE CONTEXT;24
6.1;1 Origins in Context;26
6.2;2 Relevant Literature Review;28
6.2.1;2.1 Classic Modeling and Extensions;28
6.2.2;2.2 Other Modeling Paradigms;30
6.2.3;2.3 Computational Intelligence - Soft Computing;35
6.2.4;2.4 Lattice Theory in Practice;39
7;PART II: THEORY AND ALGORITHMS;43
7.1;3 Novel Mathematical Background;44
7.1.1;3.1 Partially Ordered Sets;44
7.1.2;3.2 Elements from Lattice Theory;47
7.1.3;3.3 Positive Valuation Functions;50
7.1.4;3.4 Useful Isomorphisms in a Complete Lattice;54
7.1.5;3.5 Families of Lattice Intervals;56
7.2;4 Real-World Grounding;58
7.2.1;4.1 The Euclidean Space RN;58
7.2.2;4.2 Hyperboxes in RN;59
7.2.3;4.3 Propositional (Boolean) Logic;60
7.2.4;4.4 A Probability Space;61
7.2.5;4.5 FINs: Fuzzy Interval Numbers;62
7.2.6;4.6 Integrable Real Functions Functions Functions;80
7.2.7;4.7 Linear Metric Spaces;80
7.2.8;4.8 Structured Data Domains;83
7.2.9;4.9 Disparate Data Fusion;85
7.3;5 Knowledge Representation;86
7.3.1;5.1 Data, Semantics, and Knowledge;86
7.3.2;5.2 Tunable Lattice Semantics;89
7.4;6 The Modeling Problem and its Formulation;90
7.4.1;6.1 Models in Soft Computing;90
7.4.2;6.2 Model Unification;92
7.4.3;6.3 Optimization;93
7.5;7 Algorithms for Clustering, Classification, and Regression;94
7.5.1;7.1 Algorithms for Clustering;94
7.5.2;7.2 Algorithms for Classification;105
7.5.3;7.3 Optimized Classifier Ensembles;114
7.5.4;7.4 Algorithms for Regression;116
7.5.5;7.5 Genetic Algorithm Optimization;117
8;PART III: APPLICATIONS AND COMPARISONS;119
8.1;8 Numeric Data Applications;120
8.1.1;8.1 Artificial Data Sets;120
8.1.2;8.2 Benchmark Data Sets;123
8.1.3;8.3 Real World Applications;139
8.1.4;8.4 Discussion of the Results;145
8.2;9 Nonnumeric Data Applications;146
8.2.1;9.1 Benchmark Data Sets;146
8.2.2;9.2 Real World Applications;153
8.2.3;9.3 Discussion of the Results;163
8.3;10 Connections with Established Paradigms;164
8.3.1;10.1 Adaptive Resonance Theory;164
8.3.2;10.2 Hyperbox-based Models;170
8.3.3;10.3 Self-Organizing Maps;173
8.3.4;10.4 Various Neural Networks;175
8.3.5;10.5 Fuzzy Inference Systems;177
8.3.6;10.6 Ambiguous System Modeling;185
8.3.7;10.7 A Unified Treatment of Uncertainty;186
8.3.8;10.8 Machine Learning;189
8.3.9;10.9 Database Processing Techniques;192
8.3.10;10.10 Mathematical Connections;194
9;PART IV: CONCLUSION;197
9.1;11 Implementation Issues;198
9.1.1;11.1 Turing Machine Implementations;198
9.1.2;11.2 Beyond Turing Machine Implementations;200
9.2;12 Discussion;202
9.2.1;12.1 Contribution Highlights;202
9.2.2;12.2 Future Work Speculations;204
9.3;Epilogue;207
9.4;Appendix A: Useful Mathematical Definitions;208
9.4.1;A.1 Various Definitions;208
9.4.2;A.2 Elements from Topology;209
9.4.3;A.3 Elements from Algebra;210
9.5;Appendix B: Mathematical Proofs;212
9.5.1;B.1 Chapter 3 Proofs;212
9.5.2;B.2 Chapter 4 Proofs;218
9.5.3;B.3 Chapter 10 Proofs;221
9.6;Appendix C: Geometrical Interpretations;224
9.6.1;C.1 Inclusion Measure;224
9.6.2;C.2 FLN and the Technique of Maximal Expansions;227
9.6.3;Example E4: Utility of the technique of maximal expansions;229
10;References;232
11;Index;266