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Copyright and licensing information ii

Contents, figures and tables v

Foreword to the Second Edition xix

Acknowledgements xxi

1      Introduction and terminology 1

1.1       Motivation and Media. 1

1.1.1        Guide overview. 1

1.1.2        Spatial analysis, GIS and software tools 1

1.1.3        Intended audience and scope. 4

1.2       Software tools and Companion Materials 6

1.2.1        GIS and related software tools 6

1.2.1.1     Sample software products 7

1.2.1.2     Software performance. 7

1.2.2        Suggested reading. 11

1.3       Structure. 14

1.4       Terminology and Abbreviations 15

1.4.1        Definitions 15

1.5       Common Measures and Notation. 21

1.5.1        Notation. 21

1.5.2        Statistical measures and related formulas 23

1.5.2.1     Counts and specific values 23

1.5.2.2     Measures of centrality 24

1.5.2.3     Measures of spread. 25

1.5.2.4     Measures of distribution shape. 28

1.5.2.5     Measures of complexity and dimensionality 28

1.5.2.6     Common distributions 29

1.5.2.7     Data transforms and back transforms 30

1.5.2.8     Selected functions 31

1.5.2.9     Matrix expressions 32

2      Conceptual Frameworks for Spatial Analysis 35

2.1       The geospatial perspective. 35

2.2       Basic Primitives 36

2.2.1        Place. 36

2.2.2        Attributes 37

2.2.3        Objects 38

2.2.4        Maps 39

2.2.5        Multiple properties of places 39

2.2.6        Fields 40

2.2.7        Networks 40

2.2.8        Density estimation. 41

2.2.9        Detail, resolution, and scale. 41

2.2.10       Topology 42

2.3       Spatial Relationships 43

2.3.1        Co-location. 43

2.3.2        Distance and direction. 43

2.3.3        Multidimensional scaling. 44

2.3.4        Spatial context 44

2.3.5        Neighbourhood. 44

2.3.6        Spatial heterogeneity 45

2.3.7        Spatial dependence. 45

2.3.8        Spatial sampling. 46

2.3.9        Spatial interpolation. 46

2.3.10       Smoothing and sharpening. 47

2.3.11       First- and second-order processes 47

2.4       Spatial Statistics 49

2.4.1        Spatial probability 49

2.4.2        Probability density 49

2.4.3        Uncertainty 49

2.4.4        Statistical inference. 50

2.5       Spatial Data Infrastructure. 52

2.5.1        Geoportals 52

2.5.2        Metadata. 52

2.5.3        Interoperability 52

2.5.4        Conclusion. 52

3      Historical and Methodological Context 53

3.1       Historical Context 53

3.2       Methodological Context 56

3.2.1        Spatial analysis as a process 56

3.2.2        Analytical methodologies 57

3.2.3        Spatial analysis and the PPDAC model 61

3.2.3.1     Problem: Framing the question. 62

3.2.3.2     Plan: Formulating the approach. 63

3.2.3.3     Data: Data acquisition. 64

3.2.3.4     Analysis: Analytical methods and tools 65

3.2.3.5     Conclusions: Delivering the results 67

3.2.4        The changing context of PPDAC. 67

4      Building Blocks of Spatial Analysis 71

4.1       Spatial Data Models and Methods 71

4.2       Geometric and Related Operations 73

4.2.1        Length and area for vector datasets 73

4.2.2        Length and area for raster datasets 75

4.2.3        Surface area. 76

4.2.3.1     Projected surfaces 76

4.2.3.2     Terrestrial (unprojected) surface area. 78

4.2.4        Line Smoothing and point-weeding. 79

4.2.5        Centroids and centres 81

4.2.5.1     Polygon centroids and centres 81

4.2.5.2     Point sets 84

4.2.5.3     Lines 86

4.2.6        Point (object) in polygon (PIP) 86

4.2.7        Polygon decomposition. 87

4.2.8        Shape. 88

4.2.9        Overlay and combination operations 90

4.2.10       Areal interpolation. 93

4.2.11       Districting and re-districting. 95

4.2.12       Classification and clustering. 100

4.2.12.1    Univariate classification schemes 100

4.2.12.2    Multivariate classification and clustering. 103

4.2.12.3    Multi-band image classification. 105

4.2.12.4    Uncertainty and image processing. 110

4.2.12.5    Hyperspectral image classification. 111

4.2.13       Boundaries and zone membership. 114

4.2.13.1    Convex hulls 114

4.2.13.2    Non-convex hulls 115

4.2.13.3    Minimum Bounding Rectangles (MBRs) 117

4.2.13.4    Fuzzy boundaries 118

4.2.13.5    Breaklines and natural boundaries 121

4.2.14       Tessellations and triangulations 122

4.2.14.1    Delaunay Triangulation. 122

4.2.14.2    TINs — Triangulated irregular networks 123

4.2.14.3    Voronoi/Thiessen polygons 124

4.3       Queries and Computations 127

4.3.1        Spatial selection and spatial queries 127

4.3.2        Simple calculations 127

4.3.3        Ratios, indices, normalisation and standardisation. 130

4.3.4        Density, kernels and occupancy 134

4.3.4.1     Point density 135

4.3.4.2     Line and intersection densities 142

4.4       Distance Operations 143

4.4.1        Metrics 145

4.4.1.1     Introduction. 145

4.4.1.2     Terrestrial distances 146

4.4.1.3     Extended Euclidean and Lp-metric distances 147

4.4.2        Cost distance. 149

4.4.2.1     Accumulated cost surfaces and least cost paths 150

4.4.2.2     Distance transforms 154

4.4.3        Network distance. 158

4.4.4        Buffering. 159

4.4.4.1     Vector buffering. 159

4.4.4.2     Raster buffering. 161

4.4.4.3     Hybrid buffering. 161

4.4.4.4     Network buffering. 161

4.4.5        Distance decay models 161

4.5       Directional Operations 165

4.5.1        Directional analysis - overview. 165

4.5.2        Directional analysis of linear datasets 165

4.5.3        Directional analysis of point datasets 170

4.5.4        Directional analysis of surfaces 172

4.6       Grid Operations and Map Algebra. 173

4.6.1        Operations on single and multiple grids 173

4.6.2        Linear spatial filtering. 174

4.6.3        Non-linear spatial filtering. 178

4.6.4        Erosion and dilation. 178

5      Data Exploration and Spatial Statistics 181

5.1       Statistical Methods and Spatial Data. 181

5.1.1        Descriptive statistics 182

5.1.2        Spatial sampling. 182

5.1.2.1     Sampling frameworks 183

5.1.2.2     Declustering. 187

5.2       Exploratory Spatial Data Analysis 189

5.2.1        EDA, ESDA and ESTDA. 189

5.2.2        Outlier detection. 190

5.2.2.1     Mapped histograms 190

5.2.2.2     Box plots 191

5.2.3        Cross tabulations and conditional choropleth plots 192

5.2.4        ESDA and mapped point data. 195

5.2.5        Trend analysis of continuous data. 196

5.2.6        Cluster hunting. 196

5.3       Grid-based Statistics 198

5.3.1        Overview of grid-based statistics 198

5.3.2        Crosstabulated grid data. 199

5.3.3        Quadrat analysis of grid datasets 201

5.3.4        Landscape Metrics 202

5.3.4.1     Non-spatial metrics 205

5.3.4.2     Spatial metrics 205

5.3.4.3     Landscape metrics — table of metrics 208

5.4       Point Sets and Distance Statistics 211

5.4.1        Basic distance-derived statistics 211

5.4.2        Nearest neighbour methods 211

5.4.3        Hot spot and cluster analysis 218

5.4.3.1     Hierarchical nearest neighbour clustering. 219

5.4.3.2     K-means clustering. 220

5.4.3.3     Kernel density clustering. 220

5.5       Spatial Autocorrelation. 222

5.5.1        Autocorrelation, time series and spatial analysis 222

5.5.2        Global spatial autocorrelation. 223

5.5.2.1     Join counts 223

5.5.2.2     Moran I and Geary C. 227

5.5.2.3     Weighting models and lags 234

5.5.3        Local indicators of spatial association (LISA) 235

5.5.4        Significance tests for autocorrelation indices 237

5.6       Regression Methods 239

5.6.1        Regression overview. 239

5.6.2        Simple regression and trend surface modelling. 244

5.6.3        Geographically Weighted Regression (GWR) 246

5.6.4        Spatial autoregressive and Bayesian modelling. 250

5.6.4.1     Spatial autoregressive modelling. 250

5.6.4.2     Conditional autoregressive and Bayesian modelling. 252

5.6.5        Spatial filtering models 255

6      Surface and Field Analysis 257

6.1       Modelling Surfaces 257

6.1.1        Test datasets 257

6.1.2        Surfaces and fields 258

6.1.3        Raster models 259

6.1.4        Vector models 262

6.1.5        Mathematical models 263

6.1.6        Statistical and fractal models 264

6.2       Surface Geometry. 267

6.2.1        Gradient, slope and aspect 267

6.2.1.1     Slope. 267

6.2.1.2     Aspect 269

6.2.2        Profiles and curvature. 272

6.2.2.1     Profiles and cross-sections 272

6.2.2.2     Curvature and morphometric analysis 272

6.2.2.3     Profile curvature. 275

6.2.2.4     Plan curvature. 275

6.2.2.5     Tangential curvature. 276

6.2.2.6     Longitudinal and cross-sectional curvature. 276

6.2.2.7     Mean, maximum and minimum curvature. 276

6.2.3        Directional derivatives 276

6.2.4        Paths on surfaces 277

6.2.5        Surface smoothing. 278

6.2.6        Pit filling. 279

6.2.7        Volumetric analysis 280

6.3       Visibility. 281

6.3.1        Viewsheds and RF propagation. 281

6.3.2        Line of sight 284

6.3.3        Isovist analysis 285

6.4       Watersheds and Drainage. 287

6.4.1        Overview of watersheds and drainage. 287

6.4.2        Drainage modelling. 287

6.4.3        D-infinity model 288

6.4.4        Drainage modelling case study 289

6.4.4.1     Flow accumulation. 289

6.4.4.2     Stream network construction. 289

6.4.4.3     Stream basin construction. 290

6.5       Gridding, Interpolation and Contouring. 291

6.5.1        Overview of gridding and interpolation. 291

6.5.2        Gridding and interpolation methods 292

6.5.2.1     Comparison of sample gridding and interpolation methods 292

6.5.2.2     Contour plots of sample gridding and interpolation methods 295

6.5.3        Contouring. 298

6.6       Deterministic Interpolation Methods 300

6.6.1        Inverse distance weighting (IDW) 301

6.6.2        Natural neighbour 302

6.6.3        Nearest-neighbour 305

6.6.4        Radial basis and spline functions 305

6.6.5        Modified Shepard. 306

6.6.6        Triangulation with linear interpolation. 307

6.6.7        Triangulation with spline-like interpolation. 307

6.6.8        Rectangular or bi-linear interpolation. 308

6.6.9        Profiling. 308

6.6.10       Polynomial regression. 308

6.6.11       Minimum curvature. 308

6.6.12       Moving average. 309

6.6.13       Local polynomial 309

6.6.14       Topogrid/Topo to raster 309

6.7       Geostatistical Interpolation Methods 311

6.7.1        Core concepts 311

6.7.1.1     Geostatistics 311

6.7.1.2     Geostatistical references 312

6.7.1.3     Semivariance. 312

6.7.1.4     Sample size. 313

6.7.1.5     Support 313

6.7.1.6     Declustering. 314

6.7.1.7     Variogram. 314

6.7.1.8     Stationarity 314

6.7.1.9     Sill, range and nugget 314

6.7.1.10    Transformation. 315

6.7.1.11    Anisotropy 316

6.7.1.12    Indicator semivariance. 317

6.7.1.13    Cross-semivariance. 317

6.7.1.14    Comments on geostatistical software packages 317

6.7.1.15    Semivariance modelling. 319

6.7.1.16    Fractal analysis 322

6.7.1.17    Madograms and Rodograms 322

6.7.1.18    Periodograms and Fourier analysis 322

6.7.2        Kriging interpolation. 323

6.7.2.1     Core process 323

6.7.2.2     Goodness of fit 325

6.7.2.3     Simple Kriging. 325

6.7.2.4     Ordinary Kriging. 325

6.7.2.5     Universal Kriging. 326

6.7.2.6     Median-Polishing and Kriging. 326

6.7.2.7     Indicator Kriging. 327

6.7.2.8     Probability Kriging. 327

6.7.2.9     Disjunctive Kriging. 327

6.7.2.10    Stratified Kriging. 327

6.7.2.11    Co-Kriging. 328

6.7.2.12    Factorial Kriging. 328

6.7.2.13    Conditional simulation. 328

7      Network and Location Analysis 331

7.1       Introduction to Network and Location Analysis 331

7.1.1        Overview of network and location analysis 331

7.1.2        Terminology 331

7.1.3        Source data. 333

7.1.4        Algorithms and computational complexity theory 334

7.2       Key Problems in Network and Location Analysis 336

7.2.1        Overview — network analysis 336

7.2.1.1     Key problems in network analysis 337

7.2.1.2     Network analysis software. 340

7.2.1.3     Key problems in location analysis 343

7.2.2        Heuristic and meta-heuristic algorithms 345

7.2.2.1     Greedy heuristics and local search. 346

7.2.2.2     Interchange heuristics 347

7.2.2.3     Metaheuristics 348

7.2.2.4     Tabu search. 348

7.2.2.5     Cross-entropy (CE) methods 349

7.2.2.6     Simulated annealing. 349

7.2.2.7     Lagrangian multipliers and Lagrangian relaxation. 350

7.2.2.8     Ant systems and ant colony optimisation (ACO) 353

7.3       Network Construction, Optimal Routes and Optimal Tours 355

7.3.1        Minimum spanning tree. 355

7.3.2        Gabriel network. 356

7.3.3        Steiner trees 358

7.3.4        Shortest (network) path problems 359

7.3.4.1     Overview of shortest path problems 359

7.3.4.2     Dantzig algorithm. 360

7.3.4.3     Dijkstra algorithm. 361

7.3.4.4     A* algorithm. 361

7.3.4.5     GIS implementations of SPAs 361

7.3.4.6     Further SPAs applications 363

7.3.5        Tours, travelling salesman problems and vehicle routing. 364

7.3.5.1     Capacitated vehicle routing. 367

7.4       Location and Service Area Problems 369

7.4.1        Location problems 369

7.4.2        Larger p-median and p-centre problems 372

7.4.2.1     Simple heuristics 372

7.4.2.2     Lagrangian relaxation. 372

7.4.2.3     Comparison of alternative p-median heuristics 375

7.4.3        Service areas 377

7.4.3.1     Travel time zones 378

7.5       Arc Routing. 380

7.5.1        Network traversal problems 380

8      Geocomputational methods and modelling 383

8.1       Introduction to Geocomputation. 383

8.1.1        Geocomputational methods 383

8.1.2        Modelling dynamic processes within GIS. 384

8.1.2.1     Representing time and change within GIS. 385

8.1.2.2     Linkage/coupling versus integration/embedding. 387

8.2       Geosimulation. 390

8.2.1        Introduction to geosimulation. 390

8.2.2        Cellular automata (CA) 390

8.2.3        Agents and agent-based models 393

8.2.3.1     Agent-based models 394

8.2.3.2     Agents 395

8.2.4        Applications of agent-based models 396

8.2.5        Advantages of agent-based models 398

8.2.6        Limitations of agent-based models 400

8.2.7        Explanation or prediction? 401

8.2.8        Developing an agent-based model 403

8.2.9        Types of simulation/modelling (s/m) systems for agent-based modelling. 404

8.2.10       Guidelines for choosing a simulation/modelling (s/m) system. 406

8.2.11       Simulation/modelling (s/m) systems for agent-based modelling. 407

8.2.12       Verification and calibration of agent-based models 414

8.2.13       Validation and analysis of agent-based model outputs 415

8.3       Artificial Neural Networks (ANN) 418

8.3.1        Introduction to artificial neural networks 418

8.3.1.1     Multi-level perceptrons (MLP) 419

8.3.1.2     Learning and back-propagation for MLPs 421

8.3.1.3     MLP Example 1: Function approximation. 424

8.3.1.4     MLP Example 2: Landcover change modelling (LCM) 426

8.3.1.5     MLP Example 3: Spatial interaction modelling. 429

8.3.2        Radial basis function networks 431

8.3.3        Self organising networks 432

8.3.3.1     Self Organising Maps (SOMs) 432

8.3.3.2     SOM unsupervised classification of hyper-spectral image data. 434

8.3.3.3     Optimisation using SOM concepts 439

8.4       Genetic Algorithms and Evolutionary Computing. 441

8.4.1        Genetic algorithms — introduction. 441

8.4.2        Genetic algorithm components 442

8.4.2.1     Encoding or representation. 442

8.4.2.2     Fitness function. 443

8.4.2.3     Population initialisation. 444

8.4.2.4     Selection. 444

8.4.2.5     Reproduction. 445

8.4.2.6     Crossover 445

8.4.2.7     Mutation. 446

8.4.2.8     Local search. 446

8.4.2.9     Termination. 446

8.4.3        Example GA applications 446

8.4.3.1     GA Example 1: TSP. 446

8.4.3.2     GA Example 2: Clustering. 446

8.4.3.3     GA Example 3: Map labelling. 447

8.4.3.4     GA Example 4: Optimum location. 449

8.4.4        Evolutionary computing and genetic programming. 449

Afterword 451

References 453

Web links 473

Principal software products cited. 473

Associations and academic bodies 476

Online technical dictionaries/definitions 477

Spatial data, test data and spatial information sources 478

Selected data and information sources 478

Test datasets 478

Statistics and Spatial Statistics links 478

Trade sites 479

Index 481

 

List of Figures

Figure 2‑1 An example map showing points, lines, and areas appropriately symbolised. 39

Figure 2‑2 Topological relationships 42

Figure 2‑3 Three alternative ways of defining neighbourhood, using simple GIS functions 45

Figure 2‑4 Four distinct patterns of twelve points in a study area. 48

Figure 2‑5 The process of statistical inference. 50

Figure 3‑1 The components of a GIS. 53

Figure 3‑2 Analytical process — Mitchell 57

Figure 3‑3 Analytical process — Draper 58

Figure 3‑4 PPDAC as an iterative process 60

Figure 4‑1 Area calculation using Simpson’s rule. 73

Figure 4‑2 3x3 grid neighbourhood. 75

Figure 4‑3 5x5 grid neighbourhood. 76

Figure 4‑4 Triangular approximation of surface area. 77

Figure 4‑5 Surface model of DEM for OS TQ81NE tile. 78

Figure 4‑6 Smoothing techniques 80

Figure 4‑7 Triangle centroid. 82

Figure 4‑8 Polygon centroid (M2) and alternative polygon centres 82

Figure 4‑9 Centre and centroid positioning. 83

Figure 4‑10 Polygon centre selection. 84

Figure 4‑11 Point set centres 85

Figure 4‑12 Point in polygon — tests and special cases 86

Figure 4‑13 Skeletonised