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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley Series in Probability and Statistics
- Sprache: Englisch
A comprehensive overview of the internationalisation of correspondence analysis
Correspondence Analysis: Theory, Practice and New Strategies examines the key issues of correspondence analysis, and discusses the new advances that have been made over the last 20 years.
The main focus of this book is to provide a comprehensive discussion of some of the key technical and practical aspects of correspondence analysis, and to demonstrate how they may be put to use. Particular attention is given to the history and mathematical links of the developments made. These links include not just those major contributions made by researchers in Europe (which is where much of the attention surrounding correspondence analysis has focused) but also the important contributions made by researchers in other parts of the world.
Key features include:
- A comprehensive international perspective on the key developments of correspondence analysis.
- Discussion of correspondence analysis for nominal and ordinal categorical data.
- Discussion of correspondence analysis of contingency tables with varying association structures (symmetric and non-symmetric relationship between two or more categorical variables).
- Extensive treatment of many of the members of the correspondence analysis family for two-way, three-way and multiple contingency tables.
Correspondence Analysis offers a comprehensive and detailed overview of this topic which will be of value to academics, postgraduate students and researchers wanting a better understanding of correspondence analysis. Readers interested in the historical development, internationalisation and diverse applicability of correspondence analysis will also find much to enjoy in this book.
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Veröffentlichungsjahr: 2014
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CONTENTS
Cover
Wiley Series in Probability and Statistics
Title Page
Copyright
Dedication
Foreword
Preface
Part One: Introduction
Chapter 1: Data Visualisation
1.1 A Very Brief Introduction to Data Visualisation
1.2 Data Visualisation for Contingency Tables
1.3 Other Plots
1.4 Studying Exposure to Asbestos
1.5 Happiness Data
1.6 Correspondence Analysis Now
1.7 Overview of the Book
1.8 R Code
References
Chapter 2: Pearson's Chi-Squared Statistic
2.1 Introduction
2.2 Pearson's Chi-Squared Statistic
2.3 The Goodman–-Kruskal Tau Index
2.4 The 2 × 2 Contingency Table
2.5 Early Contingency Tables
2.6 R Code
References
Part Two: Correspondence Analysis of Two-Way Contingency Tables
Chapter 3: Methods of Decomposition
3.1 Introduction
3.2 Reducing Multidimensional Space
3.3 Profiles and Cloud of Points
3.4 Property of Distributional Equivalence
3.5 The Triplet and Classical Reciprocal Averaging
3.6 Solving the Triplet Using Eigen-Decomposition
3.7 Solving the Triplet Using Singular Value Decomposition
3.8 The Generalised Triplet and Reciprocal Averaging
3.9 Solving the Generalised Triplet Using Gram–Schmidt Process
3.10 Bivariate Moment Decomposition
3.11 Hybrid Decomposition
3.12 R Code
3.13 A Preliminary Graphical Summary
3.14 Analysis of Analgesic Drugs
References
Chapter 4: Simple Correspondence Analysis
4.1 Introduction
4.2 Notation
4.3 Measuring Departures from Complete Independence
4.4 Decomposing the Pearson Ratio
4.5 Coordinate Systems
4.6 Distances
4.7 Transition Formulae
4.8 Moments of the Principal Coordinates
4.9 How Many Dimensions to Use?
4.10 R Code
4.11 Other Theoretical Issues
4.12 Some Applications of Correspondence Analysis
4.13 Analysis of a Mother's Attachment to Her Child
References
Chapter 5: Non-Symmetrical Correspondence Analysis
5.1 Introduction
5.2 The Goodman–Kruskal Tau Index
5.3 Non-Symmetrical Correspondence Analysis
5.4 The Coordinate Systems
5.5 Transition Formulae
5.6 Moments of the Principal Coordinates
5.7 The Distances
5.8 Comparison with Simple Correspondence Analysis
5.9 R Code
5.10 Analysis of a Mother's Attachment to Her Child
References
Chapter 6: Ordered Correspondence Analysis
6.1 Introduction
6.2 Pearson's Ratio and Bivariate Moment Decomposition
6.3 Coordinate Systems
6.4 Artificial Data Revisited
6.5 Transition Formulae
6.6 Distance Measures
6.7 Singly Ordered Analysis
6.8 R Code
References
Chapter 7: Ordered Non-Symmetrical Correspondence Analysis
7.1 Introduction
7.2 General Considerations
7.3 Doubly Ordered Non-Symmetrical Correspondence Analysis
7.4 Singly Ordered Non-Symmetrical Correspondence Analysis
7.5 Coordinate Systems for Ordered Non-Symmetrical Correspondence Analysis
7.6 Tests of Asymmetric Association
7.7 Distances in Ordered Non-Symmetrical Correspondence Analysis
7.8 Doubly Ordered Non-Symmetrical Correspondence of Asbestos Data
7.9 Singly Ordered Non-Symmetrical Correspondence Analysis of Drug Data
7.10 R Code for Ordered Non-Symmetrical Correspondence Analysis
References
Chapter 8: External Stability and Confidence Regions
8.1 Introduction
8.2 On the Statistical Significance of a Point
8.3 Circular Confidence Regions for Classical Correspondence Analysis
8.4 Elliptical Confidence Regions for Classical Correspondence Analysis
8.5 Confidence Regions for Non-Symmetrical Correspondence Analysis
8.6 Approximate p-Values and Classical Correspondence Analysis
8.7 Approximate p-Values and Non-Symmetrical Correspondence Analysis
8.8 Bootstrap Elliptical Confidence Regions
8.9 Ringrose's Bootstrap Confidence Regions
8.10 Confidence Regions and Selikoff's Asbestos Data
8.11 Confidence Regions and Mother–Child Attachment Data
8.12 R Code
References
Chapter 9: Variants of Correspondence Analysis
9.1 Introduction
9.2 Correspondence Analysis Using Adjusted Standardised Residuals
9.3 Correspondence Analysis Using the Freeman–Tukey Statistic
9.4 Correspondence Analysis of Ranked Data
9.5 R Code
9.6 The Correspondence Analysis Family
9.7 Other Techniques
References
Part Three: Correspondence Analysis of Multi-Way Contingency Tables
Chapter 10: Coding and Multiple Correspondence Analysis
10.1 Introduction to Coding
10.2 Coding Data
10.3 Coding Ordered Categorical Variables by Orthogonal Polynomials
10.4 Burt Matrix
10.5 An Introduction to Multiple Correspondence Analysis
10.6 Multiple Correspondence Analysis
10.7 Variants of Multiple Correspondence Analysis
10.8 Ordered Multiple Correspondence Analysis
10.9 Applications
10.10 R Code
References
Chapter 11: Symmetrical and Non-Symmetrical Three-Way Correspondence Analysis
11.1 Introduction
11.2 Notation
11.3 Symmetric and Asymmetric Association in Three-Way Contingency Tables
11.4 Partitioning Three-Way Measures of Association
11.5 Formal Tests of Predictability
11.6 Tucker3 Decomposition for Three-Way Tables
11.7 Correspondence Analysis of Three-Way Contingency Tables
11.8 Modelling of Partial and Marginal Dependence
11.9 Graphical Representation
11.10 On the Application of Partitions
11.11 On the Application of Three-Way Correspondence Analysis
11.12 R Code
References
Part Four: The Computation of Correspondence Analysis
Chapter 12: Computing and Correspondence Analysis
12.1 Introduction
12.2 A Look Through Time
12.3 The Impact of R
12.4 Some Stand-Alone Programs
References
Index
End User License Agreement
List of Tables
Table 1.1
Table 1.2
Table 1.3
Table 1.4
Table 2.1
Table 2.2
Table 2.3
Table 2.4
Table 2.5
Table 2.6
Table 3.1
Table 3.2
Table 4.1
Table 4.2
Table 4.3
Table 4.4
Table 4.5
Table 4.6
Table 4.7
Table 4.8
Table 4.9
Table 4.10
Table 5.1
Table 5.2
Table 5.3
Table 5.4
Table 5.5
Table 5.6
Table 5.7
Table 5.8
Table 5.9
Table 5.10
Table 5.11
Table 5.12
Table 5.13
Table 5.14
Table 5.15
Table 5.16
Table 5.17
Table 5.18
Table 5.19
Table 6.1
Table 6.2
Table 6.3
Table 6.4
Table 6.5
Table 6.6
Table 6.7
Table 6.8
Table 7.1
Table 7.2
Table 7.3
Table 7.4
Table 7.5
Table 7.6
Table 7.7
Table 7.8
Table 7.9
Table 7.10
Table 7.11
Table 8.1
Table 8.2
Table 8.3
Table 8.4
Table 9.1
Table 9.2
Table 9.3
Table 10.1
Table 10.2
Table 10.3
Table 10.4
Table 10.5
Table 10.6
Table 10.7
Table 10.8
Table 10.9
Table 10.10
Table 11.1
Table 11.2
Table 11.3
Table 11.4
Table 11.5
Table 11.6
Table 11.7
Table 11.8
Table 11.9
Table 11.10
Table 11.11
Table 11.12
Table 11.13
Table 11.14
Table 11.15
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 1.6
Figure 1.7
Figure 1.8
Figure 1.9
Figure 1.10
Figure 1.11
Figure 1.12
Figure 1.13
Figure 1.14
Figure 1.15
Figure 1.16
Figure 1.17
Figure 1.18
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Figure 5.1
Figure 5.2
Figure 5.3
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 10.5
Figure 10.6
Figure 10.7
Figure 10.8
Figure 10.9
Figure 10.10
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Figure 11.6
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 12.7
Figure 12.8
Figure 12.9
Figure 12.10
Figure 12.11
Figure 12.12
Figure 12.13
Figure 12.14
Figure 12.15
Figure 12.16
Figure 12.17
Figure 12.18
Guide
Cover
Table of Contents
Begin Reading
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Wiley Series in Probability and Statistics
Established by WALTER A. SHEWHART and SAMUEL S. WILKS
Editors: David J. Balding, Noel A.C. Cressie, Garrett M. Fitzmaurice, Geof H. Givens, Harvey Goldstein, Geert Molenberghs, David W. Scott, Adrian F.M. Smith, Ruey S. Tsay, Sanford Weisberg
Editors Emeriti: J. Stuart Hunter, Iain M. Johnstone, Joseph B. Kadane, Jozef L. Teugels
A complete list of the titles in this series appears at the end of this volume.
Correspondence Analysis
Theory, Practice and New Strategies
Eric J. Beh
School of Mathematics & Physical Sciences University of Newcastle, Australia
Rosaria Lombardo
Department of Economics, Second University of Naples, Italy
This edition first published 2014
© 2014 John Wiley & Sons, Ltd
Registered office
John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.
The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.
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Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
Library of Congress Cataloging-in-Publication Data
Beh, Eric J., author.
Correspondence analysis: theory, practice and new strategies / Eric Beh, Rosaria Lombardo.
pages cm
Includes bibliographical references and index.
ISBN 978-1-119-95324-1 (hardback)
1. Correspondence analysis (Statistics) I. Lombardo, Rosaria, author. II. Title.
QA278.5.B44 2014
519.5’37–dc23
2014017301
A catalogue record for this book is available from the British Library.
ISBN: 978-1-119-95324-1
Dedication
In loving memory of my grandparents Jessie Edith and John ‘Darby’ Fortey. You may be gone but you will never be forgotten.
Eric J. Beh
Ai miei cari genitori Fortunato ed Elisabetta.
Rosaria Lombardo
Foreword
Correspondence analysis aims to lay bare the structure underlying two-way and higher way contingency tables and so allows us to explore the nature of the association between two or more categorical variables. It is not one single technique but has many variants. The authors of this book counted 26 for two-way tables alone, thus not even including those variants that are used for multiway tables. This versatility is fascinating, and led the French statistician Jean-Paul Benzécri to remark that it is
[la] méthode qui bien mieux que tout autre nous a permis de découvrir les faits de structure que recèle un tableau de données quel qu'il soit [the method which, better than any other, allows us to uncover the actual structure which underlies a data table, whatever it contains].
As Beh and Lombardo convincingly show in their book, correspondence analysis has been the subject of a never-ending stream of publications, both theoretical and applied. They mention bibliographies (until 2012) that list over 7000 publications with the term ‘correspondence analysis’ in the titles, abstracts and/or keywords. The consequence of this large body of literature is that a complete book is needed to do full justice to correspondence analysis as a tool for data analysis. Thus, it will come as no surprise that several monographs on correspondence analysis have appeared over the years.
It is impossible to speak about correspondence analysis without mentioning the French connection, because much of the initial research into its theoretical and data-analytic character was carried out in France, especially by Benzécri and his colleagues. They were also the first to publish a full-scale book on the topic (1973; not translated into English until 1992). More correspondence analysis texts have been published in French, of which those by Lebart et al. (1984) and Le Roux and Rouanet (2004) have also been translated into English. The topic made its appearance on the English academic stage as a major character when Greenacre expanded his 1978 Ph.D. thesis --supervised by Benzécri –into what was to become probably the most influential monograph in English (Greenacre, 1984). Several other books on correspondence analysis were published in English, such as those by Nishisato (1980), Murtagh (2005), and Greenacre (2010). In addition, Greenacre and Blasius published a series of proceedings from their Correspondence Analysis and Related Methods (CARME) conferences (1994, 1998, 2006, 2014). Finally, introductory texts have appeared in several languages, as well as chapters in textbooks and monographs on exploratory data analysis, of which the book by Gifi (1990) has been very influential.
Given all these volumes, why produce another book in English on correspondence analysis? In other words, what makes Beh and Lombardo's book special? Several features stand out. The book covers a large variety of extensions to correspondence analysis, which have hitherto not been available within a single integrated framework. Moreover, it includes extensive references to both earlier and contemporary literature from all walks of science –whether already well known or unnecessarily obscure.
A unique characteristic of the book is the detailed exposition of non-symmetrical correspondence analysis and its variants. This technique addresses the question of the predictability of one categorical variable, given the other categorical variable(s). Furthermore, the analysis of multiway tables receives the authors' full attention in discussions of multiple correspondence analysis and three-way extensions of standard two-way techniques. The analysis of contingency tables in which one or more variables are ordered is also treated in considerable detail. All in all, many topics are dealt with which have so far not found their way into a book, and hence have not been discussed in an integrated fashion.
Luckily for the readers, the authors did not stick to a purely technical treatment of their subjects but rather they have also provided R code for all techniques discussed in the book. Moreover, the source codes come with commentary on how to use them and how to interpret the outcomes. In this way, this book will contribute to the absorption of even the more advanced variants of correspondence analysis in the practice of substantive research. Finally, the authors seem to have achieved a synthesis of two traditions: in true French style, a fairly mathematical presentation is combined with a vivid exposition on visualization.
Pieter M. Kroonenberg
References
Gifi, A. (1990)
Nonlinear Multivariate Analysis
, John Wiley & Sons, Inc., New York.
Greenacre, M.J. (1984)
Theory and Applications of Correspondence Analysis
, Academic Press.
Greenacre, M.J. (2010)
Biplots in Practice
, Fundacon BBVA, Bilbao, Spain.
Le Roux, B. and Rouanet, H. (2004)
Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis
, Kluwer Academic Publications.
Lebart, L., Morineau, A., and Warwick, K.M. (1984)
Multivariate Descriptive Statistical Analysis
, John Wiley & Sons, Inc., New York.
Murtagh, F. (2005)
Correspondence Analysis and Data Coding with Java and R
, Chapman & Hall/CRC.
Nishisato, S. (1980)
Analysis of Categorical Data: Dual Scaling and Its Applications
, University of Toronto Press.
Quetelet, A. (1849)
Letters Addressed to H.R.H. the Grand Duke of Saxe Coburg and Gotha, on the Theory of Probabilities, as Applied to the Moral and Political Sciences
, Charles & Edwin Layton Printers.
Preface
The correspondence analysis family tree is ever growing. From its roots that lie in Europe (or the United Kingdom, depending on which perspective one takes), it has matured more rapidly over the past two decades than at any time since its development. This is largely due to the continual application of correspondence analysis in all fields of research influenced largely by the advances in computer programming facilities. The widespread use of the Internet has also helped to promote both the use of all types of exploratory data analysis, including correspondence analysis, and its world-wide exposure to data analysts. So it is appropriate to step back and take stock of the original contributions to correspondence analysis, and their importance on this development, and reflect on what impact correspondence analysis has had on the statistical and allied disciplines. It should be no surprise that core developments made in the early days of correspondence analysis still resonate with us today, and many of the key researchers still play a major role in its development. With such strong foundations, a new generation of correspondence analysts (or CA'ists) is now emerging. As a result, new ideas and perspectives are emerging. These come from not just the correspondence analysis strongholds of Europe and Japan but are now far more international –however, unfortunately, its technical evolution still remains relatively slow in some parts of the world (including Australia and New Zealand).
It should therefore be no real surprise that this book provides an overview of many of the aspects concerned with correspondence analysis. In particular, we focus on the mathematical, and practical, development of correspondence analysis for two-way and multi-way contingency tables with nominal and ordinal variables. Hence, this book describes some of the old and some of the new approaches to correspondence analysis. We do so by
providing an overview of methods (old and new) that can be used for reducing the dimensionality of the cloud of points,
discussing the classical approaches, and new strategies, concerning the technical aspects, and graphical presentation, of symmetrically and asymmetrically structured categorical variables with nominal and ordered categories,
providing an overview of the internationalisation of correspondence analysis,
describing some of the popular, and no-so-popular, variations of correspondence analysis that now exist,
emphasising the use of R to perform many of the calculations necessary to undertake correspondence analysis, and
giving a historical perspective on the development of correspondence analysis.
In order to do this, the book is arranged into four sections:
Part One gives an overview of the quantification and visualisation of categorical data.
Chapter 1
provides a history of the development of graphical techniques and introduces the data sets used as a motivating example to many of the aspects we shall discuss.
Chapter 2
briefly describes Pearson's chi-squared statistic and its characteristics.
Part Two provides a comprehensive discussion of issues concerned with the correspondence analysis of a two-way contingency table.
Chapter 3
discusses a variety of methods of decomposition of matrices, including singular value decomposition, bivariate moment decomposition and hybrid decomposition.
Chapter 4
discusses many of the technical and practical aspects concerned with the simple correspondence analysis, while
Chapter 5
provides a similar discussion of non-symmetrical correspondence analysis. Both these chapters describe the correspondence analysis of two variables with nominal categories. We expand these discussions in
Chapters 6
and
7
by considering the correspondence analysis of two-way tables with ordered categorical variables. Some inferential aspects concerned with the graphical depiction of association is given in
Chapter 8
where we describe parametric confidence regions and their associated
p
-values for points as well as non-parametric confidence regions in a low-dimensional display.
Chapter 9
gives an overview of some variations of correspondence analysis not described in the earlier chapters and describes the growth of the correspondence analysis family tree.
Part Three presents a comprehensive discussion of the correspondence analysis of multiple categorical variables.
Chapter 10
gives an overview of some of the classical techniques for dealing with nominal and ordinal categories, including the recoding of a multi-way contingency table.
Chapter 11
provides an overview of techniques for analysing symmetrically and asymmetrically structured variables as a data cube.
Part Four gives an overview of some of the computational aspects to correspondence analysis. While R is extensively used, and described, throughout the book,
Chapter 12
gives an overview of other R code that may be used. The chapter also describes the use of some popular commercially available packages and other programs that enable a variety of correspondence analysis techniques to be considered.
When reading this book, our expectation is that the reader has a fundamental understanding of statistics and linear algebra. However, where all mathematical aspects are concerned, we have tried to provide a proof of the results where needed and have given a conceptual discussion of their relevance.
This book would not have been possible without the generosity and encouragement from a host of people. We would like to thank the following people for their encouragement, guidance, discussions and help during the preparation of the book: Ida Camminatiello, Salman Cheema, Luigi D'Ambra, Irene Hudson, Pieter Kroonenberg, John Rayner, Trevor Ringrose, Duy Tran and Sidra Zafar.
We are very grateful to the generosity of the following people (listed alphabetically) for allowing us to include their photos in the book: Vartan Choulakian, Luigi D'Ambra, Michael Greenacre, William Heiser, Pieter Kroonenberg, Ludovic Lebart, Carlo Lauro, Jan de Leeuw, Jaqueline Meulman, Shizuhiko Nishisato and Yoshio Takane.
We are very much humbled by the excitement and willingness that everyone has shown in being an important part of this book. We are grateful for those photos that come from personal collections. We are indebted to those who have also given their insight, experience and expertise on various matters of the early years of correspondence analysis. However, we acknowledge that any errors (a few would have crept in no doubt) in the text are our own. We also thank Michael Greenacre for sharing with us a photo of Jean-Paul Benzécri that appears in Chapter 4 of this book.
We would like to give special credit and thanks to Pieter Kroonenberg for looking through the book when we were (nearly) finished and for many discussions on the technical and practical aspects of correspondence analysis. We would also like to give a special thanks to our Wiley project editor Richard Davies in Chichester. Our thanks also go to Kathryn Sharples and Jo Taylor at Wiley and Shikha Pahuja at Thomson Digital for their support and patience.
This book contains an accompanying website. Please visit www.wiley.com/go/correspondence_analysis.
Some Personal Acknowledgements: Eric J. Beh
I would like to express my gratitude to Pam Davy at the University of Wollongong who paved the way for me to work on correspondence analysis. While it was a happy opportunity that I was assigned to read, and report on, Michael Greenacre's Theory and Application of Correspondence Analysis for my Honours research topic in 1994, we learnt a lot together and our collaboration fed my passion for correspondence analysis and categorical data analysis. Your support, guidance and encouragement during this time and, of course, during my Ph.D. days (1995–1998) are a big part of why I do what I do. I also thank John Rayner who has been my long time mentor, co-author, colleague and friend. My first international collaborative links commenced with Luigi D'Ambra, Biagio Simonetti and (of course) Rosaria. Without your insight, experience and inspiration, many of the ideas that we discuss in this book would not have been possible.
Some Personal Acknowledgements: Rosaria Lombardo
I would like to take this opportunity to say that I am very grateful to Luigi D'Ambra and Carlo Natale Lauro at the University of Naples who introduced me to non-symmetrical correspondence analysis when I studied for my Ph.D. (1991–1994). I convey my sincere thanks to André Carlier who was at the University of Toulouse (he may be gone but he will never be forgotten) and Pieter Kroonenberg at the University of Leiden who guided me to work on multi-way correspondence analysis while I was visiting their Department for my Ph.D. research topic in 1991–1992. I also express my thanks to Jean-François Durand who, some years later, introduced me to non-linear data transformations. You all opened my mind to new perspectives on exploratory data analysis and our collaborations fed my passion for all aspects of exploratory data analysis and non-linear principal component analysis. Without your continual support, guidance and motivation, I surely would not have been what I am. Furthermore, I would like to thank my Aussie co-author, colleague and friend Eric.
Lastly, but certainly not ‘least’, we would like to thank our families for their immense patience, love and support. Our special thanks thus go to Rosey, Alex, Donato, Renato and Andrea.
Eric J. Beh
Rosaria Lombardo
Lambert Adolphe Jacques Quetelet (1796–1874)
…did not history teach us how long a time is necessary for the most beautiful discoveries to descend and make their way to the masses, where they are destined to become fixed and to produce their finest fruits.
Quetelet (1849, p. 2)
