Spatial Analysis Along Networks Statistical and Computational Methods

by Okabe, Atsuyuki; Sugihara, Kokichi

• ISBN13: 9780470770818
• ISBN10: 0470770813
• Edition: 1st
• Format: Hardcover
• Copyright: 2012-08-13
• Publisher: Wiley

Summary

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 Biography

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.

Table of Contents

Preface	p. xiii
Acknowledgements	p. xvii
Introduction	p. 1
What is network spatial analysis?	p. 1
Network events: events on and alongside networks	p. 2
Planar spatial analysis and its limitations	p. 4
Network spatial analysis and its salient features	p. 6
Review of studies of network events	p. 10
Snow's study of cholera around Broad Street	p. 10
Traffic accidents	p. 12
Roadkills	p. 14
Street crime	p. 16
Events on river networks and coastlines	p. 17
Other events on networks	p. 18
Events alongside networks	p. 19
Outline of the book	p. 20
Structure of chapters	p. 20
Questions solved by network spatial methods	p. 21
How to study this book	p. 23
Modeling spatial events on and alongside networks	p. 25
Modeling the real world	p. 26
Object-based model	p. 26
Spatial attributes	p. 27
Nonspatial attributes	p. 28
Field-based model	p. 28
Vector data model	p. 29
Raster data model	p. 30
Modeling networks	p. 31
Object-based model for networks	p. 31
Geometric networks	p. 31
Graph for a geometric network	p. 32
Field-based model for networks	p. 33
Data models for networks	p. 34
Modeling entities on network space	p. 34
Objects on and alongside networks	p. 34
Field functions on network space	p. 37
Stochastic processes on network space	p. 37
Object-based model for stochastic spatial events on network space	p. 38
Binomial point processes on network space	p. 38
Edge effects	p. 41
Uniform network transformation	p. 42
Basic computational methods for network spatial analysis	p. 45
Data structures for one-layer networks	p. 46
Planar networks	p. 46
Winged-edge data structures	p. 47
Efficient access and enumeration of local information	p. 49
Attribute data representation	p. 51
Local modifications of a network	p. 52
Inserting new nodes	p. 52
New nodes resulting from overlying two networks	p. 52
Deleting existing nodes	p. 53
Data structures for nonplanar networks	p. 54
Multiple-layer networks	p. 54
General nonplanar networks	p. 56
Basic geometric computations	p. 57
Computational methods for line segments	p. 57
Right-turn test	p. 57
Intersection test for two line segments	p. 58
Enumeration of line segment intersections	p. 58
Time complexity as a measure of efficiency	p. 59
Computational methods for polygons	p. 60
Area of a polygon	p. 60
Center of gravity of a polygon	p. 61
Inclusion test of a point with respect to a polygon	p. 61
Polygon-line intersection	p. 62
Polygon intersection test	p. 62
Extraction of a subnetwork inside a polygon	p. 63
Set-theoretic computations	p. 64
Nearest point on the edges of a polygon from a point in the polygon	p. 65
Frontage interval	p. 66
Basic computational methods on networks	p. 66
Single-source shortest paths	p. 67
Network connectivity test	p. 70
Shortest-path tree on a network	p. 71
Extended shortest-path tree on a network	p. 71
All nodes within a prespecified distance	p. 72
Center of a network	p. 72
Heap data structure	p. 73
Shortest path between two nodes	p. 77
Minimum spanning tree on a network	p. 78
Monte Carlo simulation for generating random points on a network	p. 79
Network Voronoi diagrams	p. 81
Ordinary network Voronoi diagram	p. 82
Planar versus network Voronoi diagrams	p. 82
Geometric properties of the ordinary network Voronoi diagram	p. 83
Generalized network Voronoi diagrams	p. 85
Directed network Voronoi diagram	p. 86
Weighted network Voronoi diagram	p. 88
k-th nearest point network Voronoi diagram	p. 89
Line and polygon network Voronoi diagrams	p. 91
Point-set network Voronoi diagram	p. 93
Computational methods for network Voronoi diagrams	p. 93
Multisource Dijkstra method	p. 94
Computational method for the ordinary network Voronoi diagram	p. 95
Computational method for the directed network Voronoi diagram	p. 96
Computational method for the weighted network Voronoi diagram	p. 97
Computational method for the k-th nearest point network Voronoi diagram	p. 98
Computational methods for the line and polygon network Voronoi diagrams	p. 99
Computational method for the point-set network Voronoi diagram	p. 100
Network nearest-neighbor distance methods	p. 101
Network auto nearest-neighbor distance methods	p. 102
Network local auto nearest-neighbor distance method	p. 103
Network global auto nearest-neighbor distance method	p. 104
Network cross nearest-neighbor distance methods	p. 106
:2.1 Network local cross nearest-neighbor distance method	p. 106
Network global cross nearest-neighbor distance method	p. 108
Network nearest-neighbor distance method for lines	p. 111
Computational methods for the network nearest-neighbor distance methods	p. 112
Computational methods for the network auto nearest-neighbor distance methods	p. 112
Computational methods for the network local auto nearest-neighbor distance method	p. 113
Computational methods for the network global auto nearest-neighbor distance method	p. 116
Computational methods for the network cross nearest-neighbor distance methods	p. 116
Computational methods for the network local cross nearest-neighbor distance method	p. 116
Computational methods for the network global cross nearest-neighbor distance method	p. 117
Network K function methods	p. 119
Network auto K function methods	p. 120
Network local auto K function method	p. 121
Network global auto K function method	p. 122
Network cross K function methods	p. 122
Network local cross K function method	p. 123
Network global cross K function method	p. 124
Network global Voronoi cross K function method	p. 126
Network K function methods in relation to geometric characteristics of a network	p. 127
Relationship between the shortest-path distance and the Euclidean distance	p. 127
Network global auto K function in relation to the level-of-detail of a network	p. 129
Computational methods for the network K function methods	p. 131
Computational methods for the network auto K function methods	p. 131
Computational methods for the network local auto K function method	p. 132
Computational methods for the network global auto K function method	p. 133
Computational methods for the network cross K function methods	p. 133
Computational methods for the network local cross K function method	p. 133
Computational methods for the network global cross K function method	p. 134
Computational methods for the network global Voronoi cross K function method	p. 136
Network spatial autocorrelation	p. 137
Classification of autocorrelations	p. 139
Spatial randomness of the attribute values of network cells	p. 145
Permutation spatial randomness	p. 145
Normal variate spatial randomness	p. 146
Network Moran's I statistics	p. 146
Network local Moran's I statistic	p. 147
Network global Moran's I statistic	p. 148
Computational methods for Moran's I statistics	p. 150
Network point cluster analysis and clumping method	p. 153
Network point cluster analysis	p. 155
General hierarchical point cluster analysis	p. 155
Hierarchical point clustering methods with specific intercluster distances	p. 160
Network closest-pair point clustering method	p. 160
Network farthest-pair point clustering method	p. 161
Network average-pair point clustering method	p. 161
Network point clustering methods with other intercluster distances	p. 162
Network clumping method	p. 162
Relation to network point cluster analysis	p. 162
Statistical test with respect to the number of clumps	p. 162
Computational methods for the network point cluster analysis and clumping method	p. 164
General computational framework	p. 164
Computational methods for individual intercluster distances	p. 166
Computational methods for the network closest-pair point clustering method	p. 166
Computational methods for the network farthest-pair point clustering method	p. 168
Computational methods for the network average-pair point clustering method	p. 169
Computational aspects of the network clumping method	p. 170
Network point density estimation methods	p. 171
Network histograms	p. 172
Network cell histograms	p. 172
Network Voronoi cell histograms	p. 174
Network cell-count method	p. 175
Network kernel density estimation methods	p. 177
Network kernel density functions	p. 178
Equal-split discontinuous kernel density functions	p. 181
Equal-split continuous kernel density functions	p. 183
Computational methods for network point density estimation	p. 184
Computational methods for network cell histograms with equal-length network cells	p. 184
Computational methods for equal-split discontinuous kernel density functions	p. 186
Computational methods for equal-split continuous kernel density functions	p. 190
Network spatial interpolation	p. 195
Network inverse-distance weighting	p. 197
Concepts of neighborhoods on a network	p. 197
Network inverse-distance weighting predictor	p. 198
Network kriging	p. 199
Network kriging models	p. 200
Concepts of stationary processes on a network	p. 201
Network variogram models	p. 203
Network kriging predictors	p. 206
Computational methods for network spatial interpolation	p. 209
Computational methods for network inverse-distance weighting	p. 209
Computational methods for network kriging	p. 210
Network Huff model	p. 213
Concepts of the network Huff model	p. 214
Huff models	p. 214
Dominant market subnetworks	p. 215
Huff-based demand estimation	p. 216
Huff-based locational optimization	p. 217
Computational methods for the Huff-based demand estimation	p. 217
Shortest-path tree distance	p. 218
Choice probabilities in terms of shortest-path tree distances	p. 220
Analytical formula for the Huff-based demand estimation	p. 220
Computational tasks and their time complexities for the Huff-based demand estimation	p. 221
Computational methods for the Huff-based locational optimization	p. 222
Demand function for a newly entering store	p. 223
Topologically invariant shortest-path trees	p. 224
Topologically invariant link sets	p. 225
Numerical method for the Huff-based locational optimization	p. 227
Computational tasks and their time complexities for the Huff-based locational optimization	p. 230
GIS-based tools for spatial analysis along networks and their application	p. 231
Preprocessing tools in SANET	p. 232
Tools for testing network connectedness	p. 233
Tool for assigning points to the nearest points on a network	p. 233
Tools for computing the shortest-path distances between points	p. 234
Tool for generating random points on a network	p. 234
Statistical tools in SANET and their application	p. 235
Tools for network Voronoi diagrams and their application	p. 236
Tools for network nearest-neighbor distance methods and their application	p. 237
Network global auto nearest-neighbor distance method	p. 238
Network global cross nearest-neighbor distance method	p. 239
Tools for network K function methods and their application	p. 240
Network global auto K function method	p. 241
Network global cross K function method	p. 241
Network global Voronoi cross K function method	p. 243
Network local cross K function method	p. 244
Tools for network point cluster analysis and their application	p. 245
Tools for network kernel density estimation methods and their application	p. 246
Tools for network spatial interpolation methods and their application	p. 247
References	p. 249
Index	p. 271
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