Multidimensional scaling:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London u.a.
Chapman & Hall
1994
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Monographs on statistics and applied probability
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Systemvoraussetzungen: DOS |
| Beschreibung: | X, 213 S. graph. Darst. 1 Diskette 3,5" |
| ISBN: | 0412491206 |
Internformat
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| 100 | 1 | |a Cox, Trevor F. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multidimensional scaling |c Trevor F. Cox and Michael A. A. Cox |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London u.a. |b Chapman & Hall |c 1994 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface xi
1 Introduction 1
1.1 Introduction 1
1.2 A look at data and models 3
1.2.1 Types of data 3
1.2.2 Multidimensional scaling models 5
1.3 Proximities 8
1.3.1 The metric nature of dissimilarities 14
1.3.2 Distribution of proximity coefficients 16
1.3.3 Dissimilarity of variables 16
1.4 Matrix results 18
1.4.1 The spectral decomposition 18
1.4.2 The singular value decomposition 18
1.4.3 The Moore Penrose inverse 21
2 Metric multidimensional scaling 22
2.1 Introduction 22
2.2 Classical scaling 22
2.2.1 Recovery of coordinates 23
2.2.2 Dissimilarities as Euclidean distances 25
2.2.3 Classical scaling in practice 27
2.2.4 How many dimensions? 29
2.2.5 A practical algorithm for classical scaling 29
2.2.6 A grave example 30
2.2.7 Classical scaling and principal components 34
2.2.8 The additive constant problem 35
2.3 Robustness 37
2.4 Least squares scaling 38
2.4.1 The theory for least squares scaling 39
2.4.2 Critchley s intermediate method 40
viii CONTENTS
3 Nonmetric multidimensional scaling 42
3.1 Introduction 42
3.1.1 Rp space and the Minkowski metric 44
3.2 Kruskal s approach 45
3.2.1 Minimizing S with respect to the disparities 46
3.2.2 A configuration with minimum stress 49
3.2.3 Kruskal s iterative technique 50
3.2.4 Nonmetric scaling of breakfast cereals 52
3.2.5 STRESSl/2, monotonicity, ties and
missing data 55
3.3 The Guttman approach 56
3.4 A further look at stress 58
3.4.1 Interpretation of stress 60
3.5 How many dimensions? 69
3.6 Starting configurations 70
3.7 Interesting axes in the configuration 71
4 Further aspects of multidimensional scaling 74
4.1 Robust MDS 74
4.2 Interactive MDS 76
4.3 Dynamic MDS 77
4.4 Constrained MDS 81
4.4.1 Spherical MDS 82
4.5 Statistical inference for MDS 85
4.6 Asymmetric dissimilarities 89
5 Procrustes analysis 92
5.1 Introduction 92
5.2 Procrustes analysis 92
5.2.1 Procrustes analysis in practice 96
5.3 Historic maps 96
5.4 Some generalizations 98
5.4.1 Weighted Procrustes rotation 99
5.4.2 More than two configurations 100
5.4.3 The coefficient of congruence 101
5.4.4 Oblique Procrustes problem 102
5.4.5 Perturbation analysis 103
6 Monkeys, aeroplanes, yoghurts and bees 105
6.1 Introduction 105
6.2 Monkeys 105
CONTENTS ix
6.3 Aeroplanes 107
6.4 Yoghurts 109
6.5 Bees 110
7 Unfolding 113
7.1 Introduction 113
7.2 Nonmetric unidimensional unfolding 114
7.3 Nonmetric multidimensional unfolding 116
7.4 Metric multidimensional unfolding 119
7.4.1 The rating of nations 123
8 Correspondence analysis 126
8.1 Introduction 126
8.2 Analysis of two way contingency tables 126
8.3 The theory of correspondence analysis 128
8.3.1 The cancer example 130
8.3.2 Inertia 133
8.4 Reciprocal averaging 134
8.4.1 Algorithm for solution 135
8.4.2 An example: the Miinsingen data 136
8.4.3 The correspondence analysis connection 137
8.5 Multiple correspondence analysis 137
8.5.1 A three way example 139
9 Individual differences models 142
9.1 Introduction 142
9.2 The Tucker Messick model 142
9.3 INDSCAL 143
9.3.1 The algorithm for solution 143
9.3.2 Identifying groundwater populations 145
9.3.3 Extended INDSCAL models 147
9.4 IDIOSCAL 148
9.5 PINDIS 149
10 ALSCAL and SMACOF 152
10.1 ALSCAL 152
10.1.1 The theory 152
10.1.2 Minimizing SSTRESS 154
10.2 SMACOF 156
10.2.1 The majorization algorithm 156
x CONTENTS
10.2.2 The majorizing method for nonmetric
MDS 160
10.2.3 Tunnelling for a global minimum 160
11 Further m mode, n^way models 162
11.1 CANDECOMP, PARAFAC and CANDELINC 162
11.2 The Tucker models 164
11.2.1 Relationship to other models 166
11.3 One mode, n way models 166
Appendix Computer programs for multidimensional
scaling 171
A.I Computer programs 171
A.2 The accompanying diskette 172
A.2.1 The programs 173
A.2.2 The data sets 175
A.2.3 An illustration 176
A.3 Data format 178
A.4 Error messages 181
References 187
Author index 201
Subject index 205
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:45:20Z |
| institution | BVB |
| isbn | 0412491206 |
| language | English |
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| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Chapman & Hall |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Cox, Trevor F. Verfasser aut Multidimensional scaling Trevor F. Cox and Michael A. A. Cox 1. ed. London u.a. Chapman & Hall 1994 X, 213 S. graph. Darst. 1 Diskette 3,5" txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 59 Systemvoraussetzungen: DOS Multidimensionale Skalierung (DE-588)4075090-5 gnd rswk-swf Multidimensionale Skalierung (DE-588)4075090-5 s DE-604 Cox, Michael A. A. Verfasser aut Monographs on statistics and applied probability 59 (DE-604)BV002494005 59 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006655101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cox, Trevor F. Cox, Michael A. A. Multidimensional scaling Monographs on statistics and applied probability Multidimensionale Skalierung (DE-588)4075090-5 gnd |
| subject_GND | (DE-588)4075090-5 |
| title | Multidimensional scaling |
| title_auth | Multidimensional scaling |
| title_exact_search | Multidimensional scaling |
| title_full | Multidimensional scaling Trevor F. Cox and Michael A. A. Cox |
| title_fullStr | Multidimensional scaling Trevor F. Cox and Michael A. A. Cox |
| title_full_unstemmed | Multidimensional scaling Trevor F. Cox and Michael A. A. Cox |
| title_short | Multidimensional scaling |
| title_sort | multidimensional scaling |
| topic | Multidimensionale Skalierung (DE-588)4075090-5 gnd |
| topic_facet | Multidimensionale Skalierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006655101&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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