Cluster Analysis for Data Mining and System Identification
This book presents new approaches to data mining and system identification. Algorithms that can be used for the clustering of data have been overviewed. New techniques and tools are presented for the clustering, classification, regression and visualizatio
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irkhäuser Basel · Boston · Berlin
Authors: János Abonyi University of Pannonia Department of Process Engineering PO Box 158 8200 Veszprem Hungary
Balázs Feil University of Pannonia Department of Process Engineering PO Box 158 8200 Veszprem Hungary
2000 Mathematical Subject Classification: Primary 62H30, 91C20; Secondary 62Pxx, 65C60
Library of Congress Control Number: 2007927685
Bibliographic information published by Die Deutsche Bibliothek: Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliographie; detailed bibliographic data is available in the internet at
ISBN 978-3-7643-7987-2 Birkhäuser Verlag AG, Basel · Boston · Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2007 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Cover design: Alexander Faust, Basel, Switzerland Printed in Germany ISBN 978-3-7643-7987-2
e-ISBN 978-3-7643-7988-9
987654321
www.birkhauser.ch
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1 Classical Fuzzy Cluster Analysis 1.1 Motivation . . . . . . . . . . . . . . . . . . 1.2 Types of Data . . . . . . . . . . . . . . . . . 1.3 Similarity Measures . . . . . . . . . . . . . 1.4 Clustering Techniques . . . . . . . . . . . . 1.4.1 Hierarchical Clustering Algorithms . 1.4.2 Partitional Algorithms . . . . . . . . 1.5 Fuzzy Clustering . . . . . . . . . . . . . . . 1.5.1 Fuzzy partition . . . . . . . . . . . . 1.5.2 The Fuzzy c-Means Functional . . . 1.5.3 Ways for Realizing Fuzzy Clustering 1.5.4 The Fuzzy c-Means Algorithm . . . 1.5.5 Inner-Product Norms . . . . . . . . 1.5.6 Gustafson–Kessel Algorithm . . . . . 1.5.7 Gath–Geva Clustering Algorithm . . 1.6 Cluster Analysis of Correlated Data . . . . 1.7 Validity Measures . . . . . . . . . . . . . . .
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2 Visualization of the Clustering Results 2.1 Introduction: Motivation and Methods . . . . 2.1.1 Principal Component Analysis . . . . 2.1.2 Sammon Mapping . . . . . . . . . . . 2.1.3 Kohonen Self-Organizing Maps . . . . 2.2 Fuzzy Sammon Mapping . . . . . . . . . . . . 2.2.1 Modified Sammon Mapping . . . . . . 2.2.2 Application Examples . . . . . .
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