Spatial analysis along networks : statistical and computational methods

In the real world, there are numerous and various events that occur on and alongside networks, including the occurrence of traffic accidents on highways, the location of stores alongside roads, the incidence of crime on streets and the contamination along rivers. In order to carry out analyses of those events, the researcher needs to be familiar with a range of specific techniques. Spatial Analysis Along Networks provides a practical guide to the necessary statistical techniques and their computational implementation.

Each chapter illustrates a specific technique, from Stochastic Point Processes on a Network and Network Voronoi Diagrams, to Network K-function and Point Density Estimation Methods, and the Network Huff Model. The authors also discuss and illustrate the undertaking of the statistical tests described in a Geographical Information System (GIS) environment as well as demonstrating the user-friendly free software package SANET.

Spatial Analysis Along Networks:

Presents a much-needed practical guide to statistical spatial analysis of events on and alongside a network, in a logical, user-friendly order.
Introduces the preliminary methods involved, before detailing the advanced, computational methods, enabling the readers a complete understanding of the advanced topics.
Dedicates a separate chapter to each of the major techniques involved.
Demonstrates the practicalities of undertaking the tests described in the book, using a GIS.
Is supported by a supplementary website, providing readers with a link to the free software package SANET, so they can execute the statistical methods described in the book.

Students and researchers studying spatial statistics, spatial analysis, geography, GIS, OR, traffic accident analysis, criminology, retail marketing, facility management and ecology will benefit from this book.

Author Notes

Atsuyuki Okabe , Graduate School of Engineering, University of Tokyo
Professor Okabe has been studying statistical spatial analysis for 35 years, and specifically statistical spatial analysis on a network since 1995. One of the leading authorities in the area, he has published over 100 articles, in numerous international journals. He has also authored and edited four previous books.

Kokichi Sugihara , Graduate School of Information Science and Technology, University of Tokyo
Professor Sugihara has co-authored the book on Voronoi diagrams with A. Okabe. He is also an experienced author and lecturer.

Preface	p. xiii
Acknowledgements	p. xvii
1 Introduction	p. 1
1.1 What is network spatial analysis?	p. 1
1.1.1 Network events: events on and alongside networks	p. 2
1.1.2 Planar spatial analysis and its limitations	p. 4
1.1.3 Network spatial analysis and its salient features	p. 6
1.2 Review of studies of network events	p. 10
1.2.1 Snow's study of cholera around Broad Street	p. 10
1.2.2 Traffic accidents	p. 12
1.2.3 Roadkills	p. 14
1.2.4 Street crime	p. 16
1.2.5 Events on river networks and coastlines	p. 17
1.2.6 Other events on networks	p. 18
1.2.7 Events alongside networks	p. 19
1.3 Outline of the book	p. 20
1.3.1 Structure of chapters	p. 20
1.3.2 Questions solved by network spatial methods	p. 21
1.3.3 How to study this book	p. 23
2 Modeling spatial events on and alongside networks	p. 25
2.1 Modeling the real world	p. 26
2.1.1 Object-based model	p. 26
2.1.1.1 Spatial attributes	p. 27
2.1.1.2 Nonspatial attributes	p. 28
2.1.2 Field-based model	p. 28
2.1.3 Vector data model	p. 29
2.1.4 Raster data model	p. 30
2.2 Modeling networks	p. 31
2.2.1 Object-based model for networks	p. 31
2.2.1.1 Geometric networks	p. 31
2.2.1.2 Graph for a geometric network	p. 32
2.2.2 Field-based model for networks	p. 33
2.2.3 Data models for networks	p. 34
2.3 Modeling entities on network space	p. 34
2.3.1 Objects on and alongside networks	p. 34
2.3.2 Field functions on network space	p. 37
2.4 Stochastic processes on network space	p. 37
2.4.1 Object-based model for stochastic spatial events on network space	p. 38
2.4.2 Binomial point processes on network space	p. 38
2.4.3 Edge effects	p. 41
2.4.4 Uniform network transformation	p. 42
3 Basic computational methods for network spatial analysis	p. 45
3.1 Data structures for one-layer networks	p. 46
3.1.1 Planar networks	p. 46
3.1.2 Winged-edge data structures	p. 47
3.1.3 Efficient access and enumeration of local information	p. 49
3.1.4 Attribute data representation	p. 51
3.1.5 Local modifications of a network	p. 52
3.1.5.1 Inserting new nodes	p. 52
3.1.5.2 New nodes resulting from overlying two networks	p. 52
3.1.5.3 Deleting existing nodes	p. 53
3.2 Data structures for nonplanar networks	p. 54
3.2.1 Multiple-layer networks	p. 54
3.2.2 General nonplanar networks	p. 56
3.3 Basic geometric computations	p. 57
3.3.1 Computational methods for line segments	p. 57
3.3.1.1 Right-turn test	p. 57
3.3.1.2 Intersection test for two line segments	p. 58
3.3.1.3 Enumeration of line segment intersections	p. 58
3.3.2 Time complexity as a measure of efficiency	p. 59
3.3.3 Computational methods for polygons	p. 60
3.3.3.1 Area of a polygon	p. 60
3.3.3.2 Center of gravity of a polygon	p. 61
3.3.3.3 Inclusion test of a point with respect to a polygon	p. 61
3.3.3.4 Polygon-line intersection	p. 62
3.3.3.5 Polygon intersection test	p. 62
3.3.3.6 Extraction of a subnetwork inside a polygon	p. 63
3.3.3.7 Set-theoretic computations	p. 64
3.3.3.8 Nearest point on the edges of a polygon from a point in the polygon	p. 65
3.3.3.9 Frontage interval	p. 66
3.4 Basic computational methods on networks	p. 66
3.4.1 Single-source shortest paths	p. 67
3.4.1.1 Network connectivity test	p. 70
3.4.1.2 Shortest-path tree on a network	p. 71
3.4.1.3 Extended shortest-path tree on a network	p. 71
3.4.1.4 All nodes within a prespecified distance	p. 72
3.4.1.5 Center of a network	p. 72
3.4.1.6 Heap data structure	p. 73
3.4.2 Shortest path between two nodes	p. 77
3.4.3 Minimum spanning tree on a network	p. 78
3.4.4 Monte Carlo simulation for generating random points on a network	p. 79
4 Network Voronoi diagrams	p. 81
4.1 Ordinary network Voronoi diagram	p. 82
4.1.1 Planar versus network Voronoi diagrams	p. 82
4.1.2 Geometric properties of the ordinary network Voronoi diagram	p. 83
4.2 Generalized network Voronoi diagrams	p. 85
4.2.1 Directed network Voronoi diagram	p. 86
4.2.2 Weighted network Voronoi diagram	p. 88
4.2.3 k-th nearest point network Voronoi diagram	p. 89
4.2.4 Line and polygon network Voronoi diagrams	p. 91
4.2.5 Point-set network Voronoi diagram	p. 93
4.3 Computational methods for network Voronoi diagrams	p. 93
4.3.1 Multisource Dijkstra method	p. 94
4.3.2 Computational method for the ordinary network Voronoi diagram	p. 95
4.3.3 Computational method for the directed network Voronoi diagram	p. 96
4.3.4 Computational method for the weighted network Voronoi diagram	p. 97
4.3.5 Computational method for the k-th nearest point network Voronoi diagram	p. 98
4.3.6 Computational methods for the line and polygon network Voronoi diagrams	p. 99
4.3.7 Computational method for the point-set network Voronoi diagram	p. 100
5 Network nearest-neighbor distance methods	p. 101
5.1 Network auto nearest-neighbor distance methods	p. 102
5.1.1 Network local auto nearest-neighbor distance method	p. 103
5.1.2 Network global auto nearest-neighbor distance method	p. 104
5.2 Network cross nearest-neighbor distance methods	p. 106
5 :2.1 Network local cross nearest-neighbor distance method	p. 106
5.2.2 Network global cross nearest-neighbor distance method	p. 108
5.3 Network nearest-neighbor distance method for lines	p. 111
5.4 Computational methods for the network nearest-neighbor distance methods	p. 112
5.4.1 Computational methods for the network auto nearest-neighbor distance methods	p. 112
5.4.1.1 Computational methods for the network local auto nearest-neighbor distance method	p. 113
5.4.1.2 Computational methods for the network global auto nearest-neighbor distance method	p. 116
5.4.2 Computational methods for the network cross nearest-neighbor distance methods	p. 116
5.4.2.1 Computational methods for the network local cross nearest-neighbor distance method	p. 116
5.4.2.2 Computational methods for the network global cross nearest-neighbor distance method	p. 117
6 Network K function methods	p. 119
6.1 Network auto K function methods	p. 120
6.1.1 Network local auto K function method	p. 121
6.1.2 Network global auto K function method	p. 122
6.2 Network cross K function methods	p. 122
6.2.1 Network local cross K function method	p. 123
6.2.2 Network global cross K function method	p. 124
6.2.3 Network global Voronoi cross K function method	p. 126
6.3 Network K function methods in relation to geometric characteristics of a network	p. 127
6.3.1 Relationship between the shortest-path distance and the Euclidean distance	p. 127
6.3.2 Network global auto K function in relation to the level-of-detail of a network	p. 129
6.4 Computational methods for the network K function methods	p. 131
6.4.1 Computational methods for the network auto K function methods	p. 131
6.4.1.1 Computational methods for the network local auto K function method	p. 132
6.4.1.2 Computational methods for the network global auto K function method	p. 133
6.4.2 Computational methods for the network cross K function methods	p. 133
6.4.2.1 Computational methods for the network local cross K function method	p. 133
6.4.2.2 Computational methods for the network global cross K function method	p. 134
6.4.2.3 Computational methods for the network global Voronoi cross K function method	p. 136
7 Network spatial autocorrelation	p. 137
7.1 Classification of autocorrelations	p. 139
7.2 Spatial randomness of the attribute values of network cells	p. 145
7.2.1 Permutation spatial randomness	p. 145
7.2.2 Normal variate spatial randomness	p. 146
7.3 Network Moran's I statistics	p. 146
7.3.1 Network local Moran's I statistic	p. 147
7.3.2 Network global Moran's I statistic	p. 148
7.4 Computational methods for Moran's I statistics	p. 150
8 Network point cluster analysis and clumping method	p. 153
8.1 Network point cluster analysis	p. 155
8.1.1 General hierarchical point cluster analysis	p. 155
8.1.2 Hierarchical point clustering methods with specific intercluster distances	p. 160
8.1.2.1 Network closest-pair point clustering method	p. 160
8.1.2.2 Network farthest-pair point clustering method	p. 161
8.1.2.3 Network average-pair point clustering method	p. 161
8.1.2.4 Network point clustering methods with other intercluster distances	p. 162
8.2 Network clumping method	p. 162
8.2.1 Relation to network point cluster analysis	p. 162
8.2.2 Statistical test with respect to the number of clumps	p. 162
8.3 Computational methods for the network point cluster analysis and clumping method	p. 164
8.3.1 General computational framework	p. 164
8.3.2 Computational methods for individual intercluster distances	p. 166
8.3.2.1 Computational methods for the network closest-pair point clustering method	p. 166
8.3.2.2 Computational methods for the network farthest-pair point clustering method	p. 168
8.3.2.3 Computational methods for the network average-pair point clustering method	p. 169
8.3.3 Computational aspects of the network clumping method	p. 170
9 Network point density estimation methods	p. 171
9.1 Network histograms	p. 172
9.1.1 Network cell histograms	p. 172
9.1.2 Network Voronoi cell histograms	p. 174
9.1.3 Network cell-count method	p. 175
9.2 Network kernel density estimation methods	p. 177
9.2.1 Network kernel density functions	p. 178
9.2.2 Equal-split discontinuous kernel density functions	p. 181
9.2.3 Equal-split continuous kernel density functions	p. 183
9.3 Computational methods for network point density estimation	p. 184
9.3.1 Computational methods for network cell histograms with equal-length network cells	p. 184
9.3.2 Computational methods for equal-split discontinuous kernel density functions	p. 186
9.3.3 Computational methods for equal-split continuous kernel density functions	p. 190
10 Network spatial interpolation	p. 195
10.1 Network inverse-distance weighting	p. 197
10.1.1 Concepts of neighborhoods on a network	p. 197
10.1.2 Network inverse-distance weighting predictor	p. 198
10.2 Network kriging	p. 199
10.2.1 Network kriging models	p. 200
10.2.2 Concepts of stationary processes on a network	p. 201
10.2.3 Network variogram models	p. 203
10.2.4 Network kriging predictors	p. 206
10.3 Computational methods for network spatial interpolation	p. 209
10.3.1 Computational methods for network inverse-distance weighting	p. 209
10.3.2 Computational methods for network kriging	p. 210
11 Network Huff model	p. 213
11.1 Concepts of the network Huff model	p. 214
11.1.1 Huff models	p. 214
11.1.2 Dominant market subnetworks	p. 215
11.1.3 Huff-based demand estimation	p. 216
11.1.4 Huff-based locational optimization	p. 217
11.2 Computational methods for the Huff-based demand estimation	p. 217
11.2.1 Shortest-path tree distance	p. 218
11.2.2 Choice probabilities in terms of shortest-path tree distances	p. 220
11.2.3 Analytical formula for the Huff-based demand estimation	p. 220
11.2.4 Computational tasks and their time complexities for the Huff-based demand estimation	p. 221
11.3 Computational methods for the Huff-based locational optimization	p. 222
11.3.1 Demand function for a newly entering store	p. 223
11.3.2 Topologically invariant shortest-path trees	p. 224
11.3.3 Topologically invariant link sets	p. 225
11.3.4 Numerical method for the Huff-based locational optimization	p. 227
11.3.5 Computational tasks and their time complexities for the Huff-based locational optimization	p. 230
12 GIS-based tools for spatial analysis along networks and their application	p. 231
12.1 Preprocessing tools in SANET	p. 232
12.1.1 Tools for testing network connectedness	p. 233
12.1.2 Tool for assigning points to the nearest points on a network	p. 233
12.1.3 Tools for computing the shortest-path distances between points	p. 234
12.1.4 Tool for generating random points on a network	p. 234
12.2 Statistical tools in SANET and their application	p. 235
12.2.1 Tools for network Voronoi diagrams and their application	p. 236
12.2.2 Tools for network nearest-neighbor distance methods and their application	p. 237
12.2.2.1 Network global auto nearest-neighbor distance method	p. 238
12.2.2.2 Network global cross nearest-neighbor distance method	p. 239
12.2.3 Tools for network K function methods and their application	p. 240
12.2.3.1 Network global auto K function method	p. 241
12.2.3.2 Network global cross K function method	p. 241
12.2.3.3 Network global Voronoi cross K function method	p. 243
12.2.3.4 Network local cross K function method	p. 244
12.2.4 Tools for network point cluster analysis and their application	p. 245
12.2.5 Tools for network kernel density estimation methods and their application	p. 246
12.2.6 Tools for network spatial interpolation methods and their application	p. 247
References	p. 249
Index	p. 271

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