Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis

Contents......Page 6
Foreword......Page 8
Preface......Page 10
1 Overview of Geometric Data Analysis......Page 14
1.1 CA of a Historical Data Set......Page 15
1.2 The Three Key Ideas of GDA......Page 18
1.3 Three Paradigms of GDA......Page 23
1.4 Historical Sketch......Page 24
1.5 Methodological Strong Points......Page 27
1.6 From Descriptive to Inductive Analysis......Page 30
1.7 Organization of the Book......Page 33
2 Correspondence Analysis (CA)......Page 36
2.1 Measure vs Variable Duality......Page 37
2.2 Measure over a Cartesian Product......Page 44
2.3 Correspondence Analysis......Page 49
2.4 Extensions and Concluding Comments......Page 72
Exercises......Page 78
3 Euclidean Cloud......Page 88
3.1 Basic Statistics......Page 89
3.2 Projected Clouds......Page 92
3.3 Principal Directions......Page 100
3.4 Principal Hyperellipsoids......Page 108
3.5 Between and Within Clouds......Page 113
3.6 Euclidean Classification......Page 119
3.7 Matrix Formulas......Page 129
4 Principal Component Analysis (PCA)......Page 142
4.1 Biweighted PCA......Page 145
4.2 Simple PCA......Page 162
4.3 Standard PCA......Page 163
4.4 General PCA......Page 166
4.5 PCA of a Table of Measures......Page 168
4.6 Methodology of PCA......Page 173
5 Multiple Correspondence Analysis (MCA)......Page 192
5.1 Standard MCA......Page 194
5.2 Specific MCA......Page 216
5.3 Methodology of MCA......Page 227
5.4 The Culture Example......Page 234
Exercises......Page 254
6 Structured Data Analysis......Page 264
6.1 Structuring Factors......Page 265
6.2 Analysis of Comparisons......Page 269
6.3 Additive and Interaction Clouds......Page 274
6.4 Related Topics......Page 278
7 Stability of a Euclidean Cloud......Page 282
7.1 Stability and Grouping/Effect of Coding according to a Partition......Page 283
7.2 Influence of a Group of Points......Page 290
7.3 Change of Metric......Page 294
7.4 Influence of a Variable......Page 296
7.5 Basic Theorems......Page 304
8 Inductive Data Analysis......Page 310
8.1 Inference in Multivariate Statistics......Page 311
8.2 Univariate Effects......Page 314
8.3 Combinatorial Inference......Page 323
8.4 Bayesian Data Analysis......Page 329
8.5 Inductive GDA......Page 335
8.6 Guidelines for Inductive Analysis......Page 344
9 Research Case Studies......Page 346
9.1 Parkinson Study......Page 349
9.2 French Political Space......Page 378
9.3 EPGY Study......Page 407
9.4 About Software......Page 430
10 Mathematical Bases......Page 432
10.1 Matrix Operations......Page 433
10.2 Finite–dimensional Vector Space......Page 435
10.3 Euclidean Vector Space......Page 441
10.4 Multidimensional Geometry......Page 448
10.5 Spectral Theorem......Page 455
Bibliography......Page 464
G......Page 477
P......Page 478
Y......Page 479
Symbol Index......Page 480
C......Page 482
E......Page 483
I......Page 484
M......Page 485
R......Page 486
S......Page 487
X......Page 488