Spatial Analysis along Networks: Statistical and Computational Methods

300 Pages·2012·6.07 MB·English

by  Atsuyuki Okabe

Spatial Analysis
along Networks
Statistics in Practice
Series Advisors
Human and Biological Sciences
Stephen Senn
CRP-Sant(cid:1)e, Luxembourg
Earth and Environmental Sciences
Marian Scott
University of Glasgow, UK
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Wolfgang Jank
University of Maryland, USA
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statisticsinpractice
Spatial Analysis
along Networks
Statistical and Computational Methods
Atsuyuki Okabe
School of Cultural and Creative Studies
Aoyama Gakuin University
Emeritus Professor, University of Tokyo, Japan
Kokichi Sugihara
Graduate School of Advanced Mathematical Sciences
Meiji University
Emeritus Professor, University of Tokyo, Japan
Thiseditionfirstpublished2012
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LibraryofCongressCataloging-in-PublicationData
Okabe,Atsuyuki,1945-
Spatialanalysisalongnetworks:statisticalandcomputationalmethods/AtsuyukiOkabeandKokichi
Sugihara.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-77081-8(cloth)
1. Spatialanalysis(Statistics)2. Spatialanalysis(Statistics)–Dataprocessing.3. Geography–Network
analysis. I.Sugihara,Kokichi,1948-II.Title.
QA278.2.O3592011
519.5’36–dc23
2011040047
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-0-470-77081-8
Setin10.25/12ptTimesbyThomsonDigital,Noida,India
Contents
Preface xiii
Acknowledgements xvii
1 Introduction 1
1.1 What is network spatial analysis? 1
1.1.1 Network events: events on and alongside networks 2
1.1.2 Planar spatial analysis and its limitations 4
1.1.3 Network spatial analysis and its salient features 6
1.2 Review of studies of network events 10
1.2.1 Snow’s study of cholera around Broad Street 10
1.2.2 Traffic accidents 12
1.2.3 Roadkills 14
1.2.4 Street crime 16
1.2.5 Eventson river networks and coastlines 17
1.2.6 Other events on networks 18
1.2.7 Eventsalongside networks 19
1.3 Outline of the book 20
1.3.1 Structure of chapters 20
1.3.2 Questions solved by network spatial methods 21
1.3.3 How to study this book 23
2 Modeling spatial events on and alongside networks 25
2.1 Modeling the real world 26
2.1.1 Object-based model 26
2.1.1.1 Spatial attributes 27
2.1.1.2 Nonspatial attributes 28
2.1.2 Field-based model 28
2.1.3 Vector data model 29
2.1.4 Raster data model 30
2.2 Modeling networks 31
2.2.1 Object-based model for networks 31
2.2.1.1 Geometric networks 31
2.2.1.2 Graph for a geometric network 32
2.2.2 Field-based model for networks 33
2.2.3 Data models for networks 34
vi CONTENTS
2.3 Modeling entities on network space 34
2.3.1 Objects on and alongside networks 34
2.3.2 Field functions on network space 37
2.4 Stochastic processes on network space 37
2.4.1 Object-based model for stochastic spatial events
on network space 38
2.4.2 Binomial point processes on network space 38
2.4.3 Edge effects 41
2.4.4 Uniform network transformation 42
3 Basic computational methods for network spatial analysis 45
3.1 Data structures for one-layer networks 46
3.1.1 Planar networks 46
3.1.2 Winged-edge data structures 47
3.1.3 Efficient access and enumeration of local information 49
3.1.4 Attribute data representation 51
3.1.5 Local modifications of a network 52
3.1.5.1 Inserting new nodes 52
3.1.5.2 New nodes resulting from overlying two networks 52
3.1.5.3 Deleting existing nodes 53
3.2 Data structures for nonplanar networks 54
3.2.1 Multiple-layer networks 54
3.2.2 General nonplanar networks 56
3.3 Basic geometric computations 57
3.3.1 Computational methods for line segments 57
3.3.1.1 Right-turn test 57
3.3.1.2 Intersection test for two line segments 58
3.3.1.3 Enumeration of line segment intersections 58
3.3.2 Time complexity as a measure of efficiency 59
3.3.3 Computational methods for polygons 60
3.3.3.1 Area of a polygon 60
3.3.3.2 Center of gravity of a polygon 61
3.3.3.3 Inclusion test of a point with respect to a polygon 61
3.3.3.4 Polygon-line intersection 62
3.3.3.5 Polygon intersection test 62
3.3.3.6 Extraction of a subnetwork inside a polygon 63
3.3.3.7 Set-theoretic computations 64
3.3.3.8 Nearest point on the edges of a polygon from
a point in the polygon 65
3.3.3.9 Frontage interval 66
3.4 Basic computational methods on networks 66
3.4.1 Single-source shortest paths 67
3.4.1.1 Network connectivity test 70
3.4.1.2 Shortest-path tree on a network 71
CONTENTS vii
3.4.1.3 Extended shortest-path tree on a network 71
3.4.1.4 All nodes within a prespecified distance 72
3.4.1.5 Center of a network 72
3.4.1.6 Heap data structure 73
3.4.2 Shortest path between two nodes 77
3.4.3 Minimum spanning tree on a network 78
3.4.4 Monte Carlo simulation forgenerating random
points on a network 79
4 Network Voronoi diagrams 81
4.1 Ordinary network Voronoi diagram 82
4.1.1 Planar versus network Voronoi diagrams 82
4.1.2 Geometric properties of the ordinary network Voronoi
diagram 83
4.2 Generalized network Voronoi diagrams 85
4.2.1 Directed network Voronoi diagram 86
4.2.2 Weighted network Voronoi diagram 88
4.2.3 k-th nearest point network Voronoi diagram 89
4.2.4 Line and polygon network Voronoi diagrams 91
4.2.5 Point-set network Voronoi diagram 93
4.3 Computational methods for network Voronoi diagrams 93
4.3.1 Multisource Dijkstra method 94
4.3.2 Computational method for the ordinary network
Voronoi diagram 95
4.3.3 Computational method for the directed network
Voronoi diagram 96
4.3.4 Computational method for theweighted network
Voronoi diagram 97
4.3.5 Computational method for the k-th nearest point network
Voronoi diagram 98
4.3.6 Computational methods for the line and polygon network
Voronoi diagrams 99
4.3.7 Computational method for the point-set network
Voronoi diagram 100
5 Network nearest-neighbor distance methods 101
5.1 Network auto nearest-neighbor distance methods 102
5.1.1 Network local auto nearest-neighbor distance method 103
5.1.2 Network global auto nearest-neighbor distance method 104
5.2 Network cross nearest-neighbor distance methods 106
5.2.1 Network local cross nearest-neighbor distance method 106
5.2.2 Network global cross nearest-neighbor distance method 108
5.3 Network nearest-neighbor distance method for lines 111
viii CONTENTS
5.4 Computational methods for the network nearest-neighbor
distance methods 112
5.4.1 Computational methods for the network auto
nearest-neighbor distance methods 112
5.4.1.1 Computational methods for the network
local auto nearest-neighbor distance method 113
5.4.1.2 Computational methods for the network
global auto nearest-neighbor distance method 116
5.4.2 Computational methods for the network cross
nearest-neighbor distance methods 116
5.4.2.1 Computational methods for the network local
cross nearest-neighbor distance method 116
5.4.2.2 Computational methods for the network global
cross nearest-neighbor distance method 117
6 Network K function methods 119
6.1 Network auto K function methods 120
6.1.1 Network local auto K function method 121
6.1.2 Network global auto K function method 122
6.2 Network cross K function methods 122
6.2.1 Network local cross K function method 123
6.2.2 Network global cross K function method 124
6.2.3 Network global Voronoi cross K function method 126
6.3 Network K function methods in relation to geometric
characteristics of a network 127
6.3.1 Relationship between the shortest-path distance
and the Euclidean distance 127
6.3.2 Network global auto K function in relation to the
level-of-detail of a network 129
6.4 Computational methods for the network K function methods 131
6.4.1 Computational methods for the network auto K
function methods 131
6.4.1.1 Computational methods for the network
local auto K function method 132
6.4.1.2 Computational methods for the network
global auto K function method 133
6.4.2 Computational methods for the network cross
K function methods 133
6.4.2.1 Computational methods for the network
local cross K function method 133
6.4.2.2 Computational methods for the network
global cross K function method 134
6.4.2.3 Computational methods for the network
global Voronoi cross K function method 136
CONTENTS ix
7 Network spatial autocorrelation 137
7.1 Classification of autocorrelations 139
7.2 Spatial randomness of the attributevalues of network cells 145
7.2.1 Permutation spatial randomness 145
7.2.2 Normal variate spatial randomness 146
7.3 Network Moran’s I statistics 146
7.3.1 Network local Moran’s I statistic 147
7.3.2 Network global Moran’s I statistic 148
7.4 Computational methods for Moran’s I statistics 150
8 Network point cluster analysis and clumping method 153
8.1 Network point cluster analysis 155
8.1.1 General hierarchical point cluster analysis 155
8.1.2 Hierarchical point clustering methods with specific
intercluster distances 160
8.1.2.1 Network closest-pair point clustering method 160
8.1.2.2 Network farthest-pair point clustering method 161
8.1.2.3 Network average-pair point clustering method 161
8.1.2.4 Network point clustering methods with other
intercluster distances 162
8.2 Network clumping method 162
8.2.1 Relation to network point cluster analysis 162
8.2.2 Statistical test with respect to the number of clumps 162
8.3 Computational methods for the network point cluster
analysis and clumping method 164
8.3.1 General computational framework 164
8.3.2 Computational methods for individual intercluster distances 166
8.3.2.1 Computational methods for the network
closest-pair point clustering method 166
8.3.2.2 Computational methods for the network
farthest-pair point clustering method 168
8.3.2.3 Computational methods for the network
average-pair point clustering method 169
8.3.3 Computational aspects of the network clumping method 170
9 Network point density estimation methods 171
9.1 Network histograms 172
9.1.1 Network cell histograms 172
9.1.2 Network Voronoi cell histograms 174
9.1.3 Network cell-count method 175
9.2 Network kernel density estimation methods 177
9.2.1 Network kernel density functions 178
9.2.2 Equal-split discontinuous kernel density functions 181
9.2.3 Equal-split continuous kernel density functions 183
x CONTENTS
9.3 Computational methods for network point density estimation 184
9.3.1 Computational methods for network cell histograms
with equal-length network cells 184
9.3.2 Computational methods for equal-split discontinuous
kernel density functions 186
9.3.3 Computational methods for equal-split continuous
kernel density functions 190
10 Network spatial interpolation 195
10.1 Network inverse-distanceweighting 197
10.1.1 Concepts of neighborhoods on a network 197
10.1.2 Network inverse-distanceweighting predictor 198
10.2 Network kriging 199
10.2.1 Network kriging models 200
10.2.2 Concepts of stationary processes on a network 201
10.2.3 Network variogram models 203
10.2.4 Network kriging predictors 206
10.3 Computational methods for network spatial interpolation 209
10.3.1 Computational methods for network
inverse-distanceweighting 209
10.3.2 Computational methods for network kriging 210
11 Network Huff model 213
11.1 Concepts of the network Huff model 214
11.1.1 Huff models 214
11.1.2 Dominant market subnetworks 215
11.1.3 Huff-based demand estimation 216
11.1.4 Huff-based locational optimization 217
11.2 Computational methods for the Huff-based demand estimation 217
11.2.1 Shortest-path tree distance 218
11.2.2 Choice probabilities in terms of shortest-path
tree distances 220
11.2.3 Analytical formula for the Huff-based demand
estimation 220
11.2.4 Computational tasks and their time complexities
for the Huff-based demand estimation 221
11.3 Computational methods for the Huff-based locational optimization 222
11.3.1 Demand function for a newly entering store 223
11.3.2 Topologically invariant shortest-path trees 224
11.3.3 Topologically invariant link sets 225
11.3.4 Numerical method for the Huff-based locational
optimization 227
11.3.5 Computational tasks and their time complexities
for the Huff-based locational optimization 230