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Bibliographic Details
Main Authors:	Gower, J. C. (Author), Hand, D. J. 1950- (Author)
Format:	Book
Language:	English
Published:	London u.a. Chapman & Hall 1996
Edition:	1. ed.
Series:	Monographs on statistics and applied probability 54
Subjects:	Multivariate Analysis Analise multivariada Grafische voorstellingen Statistiek Statistik Multivariate analysis > Graphic methods Multivariate Analyse Streuungsdiagramm
Online Access:	Inhaltsverzeichnis
Physical Description:	XVI, 277 S. graph. Darst.
ISBN:	0412716305

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MARC


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adam_text	BIPLOTS J.C. GOWER FORMER HEAD OF STATISTICS DEPARTMENT AND BIOMATHEMATICS DIVISION, ROTHAMSTED EXPERIMENTAL STATION, HARPENDEN, UK AND D.J. HAND PROFESSOR OF STATISTICS, OPEN UNIVERSITY, MILTON KEYNES, UK CHAPMAN & HALL LONDON * GLASGOW * WEINHEIM * NEW YORK * TOKYO * MELBOURNE * MADRAS CONTENTS PREFACE XV 1 INTRODUCTION 1.1 OVERVIEW 1.2 COMPUTATION 1.3 NOTATION 2 PRINCIPAL COMPONENTS ANALYSIS (PCA) 2.1 INTRODUCTION 2.2 FINDING THE SUBSPACE, INTERPOLATION AND PREDICTION 2.3 THE BIPLOT AXES 2.4 EQUIVALENT DEFINITIONS 2.5 HOW GOOD IS THE REPRESENTATION? 2.6 SOME PRACTICAL CONSIDERATIONS CONCERNED WITH PLOTTING VARIABLES AND SCALES 2.6.1 SCALES FOR THE VARIABLES 2.7 EXAMPLE 3 OTHER LINEAR BIPLOTS 3.1 INTRODUCTION 3.2 MULTIDIMENSIONAL SCALING (MDS) 3.3 PREDICTION 3.3.1 PROCRUSTEAN PREDICTION 3.3.2 REGRESSION BIPLOTS - PREDICTION 3.3.3 MULTIPLE AXES 3.4 INTERPOLATION 3.4.1 INTERPOLATION WITH STRESS AND SSTRESS 3.4.2 INTERPOLATION BIPLOTS BY PROJECTION 3.4.3 REGRESSION BIPLOTS - INTERPOLATION 3.5 EXAMPLES 1 1 6 6 9 9 11 13 16 16 19 22 23 31 31 32 35 35 40 41 42 42 44 45 45 X CONTENTS 4 MULTIPLE CORRESPONDENCE ANALYSIS 4.1 4.2 4.3 4.4 4.5 4.6 INTRODUCTION THE INDICATOR MATRIX MULTIPLE CORRESPONDENCE ANALYSIS (MCA) 4.3.1 CENTRING 4.3.2 CATEGORY-LEVEL-POINTS (CLPS) 4.3.3 THE BURT MATRIX OTHER APPROACHES TO MCA 4.4.1 HOMOGENEITY ANALYSIS 4.4.2 GENERALIZED CANONICAL CORRELATION ANALYSIS (GCCA) ALTERNATIVES TO % 2 DISTANCE 4.5.1 THE EXTENDED MATCHING COEFFICIENT 4.5.2 OTHER MATCHING COEFFICIENTS EXAMPLES OF MCA 5 CANONICAL BIPLOTS 5.1 5.2 5.3 5.4 5.5 5.6 INTRODUCTION CANONICAL VARIATE ANALYSIS (CVA) INTERPOLATION PREDICTION 5.4.1 PREDICTION IN THE CANONICAL SPACE 5.4.2 AN ALTERNATIVE CHARACTERIZATION 5.4.3 LINKS WITH SVD AND THE ECKART-YOUNG THEOREM CANONICAL CORRELATION BIPLOTS EXAMPLE 6 NONLINEAR BIPLOTS 6.1 6.2 6.3 6.4 6.5 6.6 INTRODUCTION ADDITIVE DDISTANCE APPROXIMATION 6.3.1 INTERPOLATION WITH EUCLIDEAN EMBEDDING 6.3.2 PREDICTION WITH EUCLIDEAN EMBEDDING THE NON-EUCLIDEAN CASE RELAXING THE ADDITIVE DDISTANCE ASSUMPTION EXAMPLES 7 GENERALIZED BIPLOTS 7.1 INTRODUCTION 51 51 52 53 54 56 57 61 61 63 65 65 71 74 86 86 86 89 90 90 92 93 95 97 102 102 105 107 107 109 113 115 116 121 121 CONTENTS XI 7.2 PSEUDOSAMPLES FOR CATEGORICAL VARIABLES 121 7.2.1 COORDINATES OF THE BASIC POINTS 123 7.2.2 JOINT MDS 130 7.3 APPROXIMATION 133 7.3.1 INTERPOLATION 133 7.3.2 PREDICTION 136 7.4 AN EXAMPLE 139 8 BIADDITIVE MODELS 142 8.1 INTRODUCTION 142 8.1.1 THE GENERALIZED BIPLOT APPROACH 142 8.1.2 INTRODUCTION TO BIADDITIVE MODELS 147 8.1.3 CONFIDENCE REGIONS FOR THE PARAMETERS OF BIADDITIVE MODELS 150 8.2 DIAGNOSTIC BIPLOTS 153 8.2.1 EXACT RANK TWO MODELS 153 8.2.2 EXACT RANK THREE AND HIGHER DIMENSIONAL MODELS 156 8.2.3 INTERESTING CROSS-SECTIONS OF THE THREE-DIMENSIONAL SPACE 164 8.2.4 OTHER THREE-DIMENSIONAL MODELS 165 8.3 PRACTICAL THREE-DIMENSIONAL DIAGNOSTIC BIPLOTS 165 8.4 AN EXAMPLE OF A BIPLOT FOR A TWO-WAY TABLE 171 9 CORRESPONDENCE ANALYSIS (CA) 175 9.1 INTRODUCTION 175 9.2 I 2 DISTANCE 176 9.3 ANALYSIS 177 9.3.1 PRINCIPAL COMPONENTS OF % 2 DISTANCE 177 9.3.2 ANALYSIS OF/ 2 179 9.3.3 CLASSICAL CA 180 9.3.4 CANONICAL CORRELATION 183 9.3.5 ABUNDANCE MATRICES AND CANONICAL CA 185 9.4 AN EXAMPLE OF CA 190 10 RELATIONSHIPS BETWEEN CA AND MCA 194 10.1 INTRODUCTION 194 10.2 CA AS THE MCA OF AN INDICATOR MATRIX FOR TWO CATEGORICAL VARIABLES 195 XII CONTENTS 10.3 JOINT CORRESPONDENCE ANALYSIS (JCA) 198 10.3.1 NON-ITERATIVE GENERALIZATION 198 10.3.2 ITERATIVE ANALYSIS 203 10.3.3 WHAT DO WE PLOT? 206 10.4 AN EXAMPLE OF JCA 207 11 OTHER TOPICS 210 11.1 INTRODUCTION 210 11.2 BIPLOTS IN NON-METRIC MDS 210 11.2.1 DISTANCE TRANSFORMATION METHODS 210 11.2.2 VARIABLE TRANSFORMATION METHODS 213 11.3 BIPLOTS IN GENERALIZED BILINEAR MODELS 215 11.4 BIPLOTS IN THREE-WAY ANALYSES 216 11.5 BIPLOTS FOR SPECIAL CLASSES OF MATRICES 220 11.5.1 THE COVARIANCE, CORRELATION AND COEFFICIENT OF VARIATION BIPLOTS 220 11.5.2 SPECIAL MATRICES 223 11.5.3 OTHER CORRELATIONAL BIPLOTS 226 11.6 REDUCED RANK REGRESSION 228 11.7 MISSING VALUES 230 APPENDIX A: ALGEBRAIC RESULTS 233 A.I SPECTRAL DECOMPOSITION 233 A.2 THE TWO-SIDED EIGENVALUE PROBLEM 235 A.3 SINGULAR VALUE DECOMPOSITION (SVD) 236 A.3.1 GENERALIZED SVD IN THE METRIC B 236 A.3.2 GENERALIZED SVD IN THE METRICS P AND Q 237 A.4 APPROXIMATION 239 A.4.1 PRINCIPAL COMPONENTS ANALYSIS (PCA) 239 A.4.2 THE ECKART-YOUNG THEOREM 241 A.4.3 ECKART-YOUNG THEOREM IN THE METRIC B 242 A.4.4 ECKART-YOUNG THEOREM IN THE METRICS P AND Q 243 A.4.5 OTHER LEAST-SQUARES APPROXIMATIONS 244 A.5 BASIC PROPERTIES OF DISTANCE MATRICES 246 A.5.1 EUCLIDEAN EMBEDDING 246 A.5.2 PRINCIPAL COORDINATES ANALYSIS (PCO) (GOWER, 1966A) 247 A.6 PARTITIONED DISTANCE MATRICES AND DISTANCES BETWEEN CENTROIDS 248 CONTENTS XIII A.6.1 DISTANCE BETWEEN THE CENTROIDS OF TWO CLOUDS OF POINTS (DIGBY AND GOWER, 1981) 248 A.6.2 DISTANCE BETWEEN THE POINTS OF ONE SET AND THE CENTROID OF A SECOND SET 249 A.7 SUPERIMPOSITION OF A POINT (INTERPOLATION) 250 A.7.1 INTERPOLATION OF ONE POINT (GOWER, 1968) 250 A.7.2 INTERPOLATION OF N 2 POINTS 252 A.8 ORTHOGONAL PROJECTION 252 A.8.1 ORTHOGONAL PROJECTION WITH AN OFFSET 254 A.8.2 ORTHOGONAL PROJECTION ONTO THE INTERSECTION OF TWO SPACES 254 A.9 BACK PROJECTION 255 A.9.1 ORTHOGONALITY RELATIONSHIPS 258 A.10 PROCRUSTES PROBLEMS 259 A. 10.1 ORTHOGONAL PROCRUSTES ANALYSIS 259 A. 10.2 AN ALGORITHM FOR MINIMAL PROJECTION ERROR PROCRUSTES ANALYSIS 260 A. 10.3 MAXIMAL GROUP-AVERAGE PROCRUSTES ANALYSIS 260 A. 11 PERRON-FROBENIUS THEOREM 261 A. 12 PROPERTIES OF THE SPACE ^ 262 A. 13 ALGORITHMS FOR CONSTRUCTING PREDICTION REGIONS 263 REFERENCES 265 INDEX 273
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author	Gower, J. C. Hand, D. J. 1950-
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ctrlnum	(OCoLC)52041509 (DE-599)BVBBV010739359
dewey-full	519.5/35
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	519 - Probabilities and applied mathematics
dewey-raw	519.5/35
dewey-search	519.5/35
dewey-sort	3519.5 235
dewey-tens	510 - Mathematics
discipline	Biologie Mathematik Wirtschaftswissenschaften
edition	1. ed.
format	Book
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spelling	Gower, J. C. Verfasser aut Biplots J. C. Gower and D. J. Hand 1. ed. London u.a. Chapman & Hall 1996 XVI, 277 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 54 Multivariate Analysis cabt Analise multivariada larpcal Grafische voorstellingen gtt Statistiek gtt Statistik Multivariate analysis Graphic methods Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Streuungsdiagramm (DE-588)4300114-2 gnd rswk-swf Streuungsdiagramm (DE-588)4300114-2 s Multivariate Analyse (DE-588)4040708-1 s DE-604 Hand, D. J. 1950- Verfasser (DE-588)123535492 aut Monographs on statistics and applied probability 54 (DE-604)BV002494005 54 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007170748&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Gower, J. C. Hand, D. J. 1950- Biplots Monographs on statistics and applied probability Multivariate Analysis cabt Analise multivariada larpcal Grafische voorstellingen gtt Statistiek gtt Statistik Multivariate analysis Graphic methods Multivariate Analyse (DE-588)4040708-1 gnd Streuungsdiagramm (DE-588)4300114-2 gnd
subject_GND	(DE-588)4040708-1 (DE-588)4300114-2
title	Biplots
title_auth	Biplots
title_exact_search	Biplots
title_full	Biplots J. C. Gower and D. J. Hand
title_fullStr	Biplots J. C. Gower and D. J. Hand
title_full_unstemmed	Biplots J. C. Gower and D. J. Hand
title_short	Biplots
title_sort	biplots
topic	Multivariate Analysis cabt Analise multivariada larpcal Grafische voorstellingen gtt Statistiek gtt Statistik Multivariate analysis Graphic methods Multivariate Analyse (DE-588)4040708-1 gnd Streuungsdiagramm (DE-588)4300114-2 gnd
topic_facet	Multivariate Analysis Analise multivariada Grafische voorstellingen Statistiek Statistik Multivariate analysis Graphic methods Multivariate Analyse Streuungsdiagramm
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007170748&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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