Biplots:
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
London u.a.
Chapman & Hall
1996
|
Ausgabe: | 1. ed. |
Schriftenreihe: | Monographs on statistics and applied probability
54 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XVI, 277 S. graph. Darst. |
ISBN: | 0412716305 |
Internformat
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Datensatz im Suchindex
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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
|
any_adam_object | 1 |
author | Gower, J. C. Hand, D. J. 1950- |
author_GND | (DE-588)123535492 |
author_facet | Gower, J. C. Hand, D. J. 1950- |
author_role | aut aut |
author_sort | Gower, J. C. |
author_variant | j c g jc jcg d j h dj djh |
building | Verbundindex |
bvnumber | BV010739359 |
callnumber-first | Q - Science |
callnumber-label | QA278 |
callnumber-raw | QA278 |
callnumber-search | QA278 |
callnumber-sort | QA 3278 |
callnumber-subject | QA - Mathematics |
classification_rvk | QH 234 SK 840 WC 7000 |
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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id | DE-604.BV010739359 |
illustrated | Illustrated |
indexdate | 2024-07-09T17:58:03Z |
institution | BVB |
isbn | 0412716305 |
language | English |
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physical | XVI, 277 S. graph. Darst. |
publishDate | 1996 |
publishDateSearch | 1996 |
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publisher | Chapman & Hall |
record_format | marc |
series | Monographs on statistics and applied probability |
series2 | Monographs on statistics and applied probability |
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 |
volume_link | (DE-604)BV002494005 |
work_keys_str_mv | AT gowerjc biplots AT handdj biplots |