Thematic Cartography, Volume 2, Cartography and the Impact of the Quantitative Revolution

General Introduction ix

PART I. TRANSFORMATIONS OF ATTRIBUTES [Z] AND USE OF QUANTITATIVE METHODS: GENERALIZATION AND MODELING 1

Part I. Introduction 3

Chapter 1. From the Description to the Generalization of an Attribute Variable Z 7

1.1. Preliminary data analysis: a crucial step 8

1.1.1. From classical description to exploratory data analysis (EDA) 8

1.1.2. Exploratory data analysis and graphical representations 11

1.1.3. Quantitative level of measurement and graphical representation 19

1.2. Discretization: a constraint with several choices 21

1.2.1. From data to the basic rules 22

1.2.2. Choice of the number of classes 23

1.2.3. Class limits and ranges 26

1.2.4. Discretization and transformation of a variable 46

1.3. Two essential requirements: choosing and assessing the methods 53

1.3.1. A logic of reasoning 55

1.3.2. Guidance for making the necessary choice 56

1.3.3. Guidance and suggestions for making the decision 66

1.4. Conclusion 74

Chapter 2. Generalization of Thematic Attributes 77

2.1. Graphical transformations of reduction and generalization 80

2.1.1. Shared characteristics and constraints of graphical processing techniques 80

2.1.2. Techniques for quantitative variables 84

2.1.3. Graphical techniques for multiple and mixed variables: taxonomic tree, scalogram, seriated matrix 107

2.2. From mathematical structuring to standardized cartographic results 118

2.2.1. A factorial method for quantitative variables 121

2.2.2. Methods for frequencies and mixed variables 129

2.3. From mathematical classifications to the interpretation of the results 137

2.3.1. Principles and review of classifications. 137

2.3.2. Representations and hierarchical classifications 140

2.3.3. Non-hierarchical classifications 145

2.4. Conclusion 147

Chapter 3. Modeling Thematic Attributes: Generalizable Cartographic Choices 149

3.1. Thematic models based on the concept of regression 150

3.1.1. Common characteristics to regression models and to their representations 150

3.1.2. Basic model: simple regression 156

3.1.3. From statistical logic to thematic logic 164

3.2. Models incorporating space via calculations 181

3.2.1. A model linked to the concept of regression: trend surfaces 181

3.2.2. A model integrating spatial component via distance: the potential model 191

3.3. Models incorporating space by construction and by calculations 197

3.3.1. A model of spatial interaction: the isochronous gravity model 197

3.3.2. A model based on the DAI - cellular automata - a method of simulating the evolution of geographic space 208

3.4. Conclusion 213

Part I. Conclusion 215

PART II. NEW CARTOGRAPHIC TRANSFORMATIONS AND 3D REPRESENTATIONS 219

Part II. Introduction 221

Chapter 4. Cartographic Transformations of Position 223

4.1. Cartographic transformations of position: aims and characteristics 224

4.1.1. Double objectives 227

4.1.2. Characteristics 229

4.2. Thematic CTPs of weight 233

4.2.1. Characteristics and classification criteria 235

4.2.2. Area cartograms: design and applications 237

4.3. Thematic CTPs of links and directions 252

4.3.1. Unipolar thematic CTPs of links and directions 253

4.3.2. Multi-polar thematic CTPs of connections 263

4.4. Differential CTPs or CTPs of comparison 267

4.4.1. Steps of bidimensional regression 268

4.4.2. Results and contributions of bidimensional regression 272

4.5. Conclusion 276

Chapter 5. Taking a Third Dimension into Account, Transformation of Display 277

5.1. From perception of relief to the diversity of "3D" products 280

5.1.1. Vision and perception in 3D: understanding and grasping depth 281

5.1.2. Conventional 3D cartographic representations 282

5.1.3. Diversity and classification of 3D images 290

5.2. Basic principles of representations with a third dimension 296

5.2.1. A constraint: the use of projection 296

5.2.2. Basic parameters of 3D representations 299

5.2.3. Specific principles depending on the continuity property 310

5.3. DTMs as examples of possibilities of DSMs 318

5.3.1. From the first digital attempts to establishing the vocabulary 319

5.3.2. Modern DTMs 321

5.3.3. Derived data and associated cartography 333

5.4. A new way: true 3D 339

5.4.1. The true 3D: basic principles 340

5.4.2. Examples and usefulness of true 3D representations 344

5.5. Conclusion 348

Part II. Conclusion 351

General conclusion 353

Bibliography 355

Software used 389

Appendices 391

Appendix 1. Table of standardized normal distribution 393

Appendix 2. Critical values of Bravais-Pearson's correlation coefficient R 394

Appendix 3. Critical values of Student's t 395

Appendix 4a. Critical values of Fisher-Snedecor's F, significance level 0.05 396

Appendix 4b. Critical values of Fisher-Snedecor's F, significance level 0.01 397

List of Authors 399

Index 401