Spatial Analysis Along Networks: Statistical and Computational MethodsISBN: 9780470770818
306 pages
August 2012

Each chapter illustrates a specific technique, from Stochastic Point Processes on a Network and Network Voronoi Diagrams, to Network Kfunction 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 userfriendly free software package SANET.
Spatial Analysis Along Networks:
 Presents a muchneeded practical guide to statistical spatial
analysis of events on and alongside a network, in a logical,
userfriendly 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.
Acknowledgements
Chapter 1 Introduction
1.1 What is network spatial analysis?
1.1.1 Network events: events on and alongside networks
1.1.2 Planar spatial analysis and its limitations
1.1.3 Network spatial analysis and its salient features
1.2 Review of studies of network events
1.2.1 Snow’s study on cholera around Broad Street
1.2.2 Traffic accidents
1.2.3 Roadkills
1.2.4 Street crimes
1.2.5 Events on river networks and coastlines
1.2.6 Other events on networks
1.2.7 Events alongside networks
1.3 Outline of the book
1.3.1 Structure of chapters
1.3.2 Questions solved by network spatial methods
1.3.3 How to study this book
Chapter 2 Modeling events on and alongside networks
2.1 Modeling the real world
2.1.1 Objectbased model
2.1.1.1 Spatial attributes
2.1.1.2 Nonspatial attributes
2.1.2 Fieldbased model
2.1.3 Vector data model
2.1.4 Raster data model
2.2 Modeling networks
2.2.1 Objectbased model for networks
2.2.1.1 Geometric networks
2.2.1.2 Graph for a geometric network
2.2.2 Fieldbased model for networks
2.2.3 Data models for networks
2.3 Modeling entities on and alongside networks
2.3.1 Objects on network space
2.3.2 Field functions on network space
2.4 Stochastic processes on network space
2.4.1 Objectbased model for stochastic spatial events on network space
2.4.2 Binomial point processes on network space
2.4.3 Edge effects
2.4.4 Uniform network transformation
Chapter 3 Basic computational methods for network spatial analysis
3.1 Data structures for onelayer networks
3.1.1 Planar networks
3.1.2 Wingededge data structures
3.1.3 Efficient access and enumeration of local information
3.1.4 Attribute data representation
3.1.5 Local modifications of a network
3.1.5.1 Inserting new nodes
3.1.5.2 New nodes resulting from overlying two networks
3.1.5.3 Deleting existing nodes
3.2 Data Structures for nonplanar networks
3.2.1 Multiplelayer networks
3.2.2 General nonplanar networks
3.3 Basic Geometric Computations
3.3.1 Computational methods for line segments
3.3.1.1 Rightturn test
3.3.1.2 Intersection test for two line segments
3.3.1.3 Enumeration of line segment intersections
3.3.2 Time complexity as a measure of efficiency
3.3.3 Computational methods for polygons
3.3.3.1 Area of a polygon
3.3.3.2 Center of gravity of a polygon
3.3.3.3 Inclusion test of a point with respect to a polygon
3.3.3.4 Polygonline intersection
3.3.3.5 Polygon intersection test
3.3.3.6 Extraction of a subnetwork inside a polygon
3.3.3.7 Settheoretic computations
3.3.3.8 Nearest point on the edges of a polygon from a point in the polygon
3.3.3.9 Frontage interval
3.4. Basic computational methods on networks
3.4.1 Singlesource shortest paths
3.4.1.1 Network connectivity test
3.4.1.2 Shortestpath tree
3.4.1.3 Extended shortestpath tree
3.4.1.4 All nodes within a prespecified distance
3.4.1.5 Center of a network
3.4.1.6 Heap data structure
3.4.2 Shortest path between two nodes
3.4.3 Minimum spanning tree on a network
3.4.4 Monte Carlo simulation for generating random points on a network
Chapter 4 Network Voronoi diagrams
4.1 Ordinary network Voronoi diagram
4.1.1 Planar versus network Voronoi diagrams
4.1.2 Geometric properties of the ordinary network Voronoi diagram
4.2 Generalized network Voronoi diagrams
4.2.1 Directed network Voronoi diagram
4.2.2 Weighted network Voronoi diagram
4.2.3 kth nearest point network Voronoi diagram
4.2.4 Line and polygon network Voronoi diagram
4.2.5 Pointset network Voronoi diagram
4.3 Computational methods for network Voronoi diagrams
4.3.1 Multistart Dijkstra method
4.3.2 Computational method for the ordinary network Voronoi diagram
4.3.3 Computational method for the directed network Voronoi diagram
4.3.4 Computational method for the weighted network Voronoi diagram
4.3.5 Computational method for the th nearest point network Voronoi diagram
4.3.6 Computational method for the line and polygon network Voronoi diagrams
4.3.7 Computational method for the pointset network Voronoi diagram
Chapter 5 Network nearestneighbor distance methods
5.1 Network auto nearestneighbor distance method
5.1.1 Network local auto nearestneighbor distance method
5.1.2 Network global auto nearestneighbor distance method
5.2 Network cross nearestneighbor distance method
5.2.1 Network local cross nearestneighbor distance method
5.2.2 Network global cross nearestneighbor distance method
5.3 Network nearestneighbor distance method for lines
5.4 Computational methods for network nearestneighbor distance methods
5.4.1 Computational methods for network auto nearestneighbor distance methods
5.4.1.1 Computational methods for network local auto nearestneighbor distance method
5.4.1.2 Computational methods for network global auto nearestneighbor distance method
5.4.2 Computational methods for network cross nearestneighbor distance methods
5.4.2.1 Computational methods for network local cross nearestneighbor distance method
5.4.2.2 Computational methods for network global cross nearestneighbor distance method
Chapter 6 Network K function methods
6.1 Network auto K function methods
6.1.1 Network local auto K function method
6.1.2 Network global auto K function method
6.2 Network cross K function methods
6.2.1 Network local cross K function method
6.2.2 Network global cross K function method
6.2.3 Network global Voronoi cross K function
method
6.3 Network K function methods in relation to geometric
characteristics of a network
6.3.1 Relationship between the shortestpath distance and the
Euclidean distance
6.3.2 Network global auto K function in relation to the
levelofdetail of a network
6.4 Computational methods for the network K function methods
6.4.1 Computational methods for the network auto K function methods
6.4.1.1 Computational methods for the network local auto K function method
6.4.1.2 Computational methods for the network global auto
K function
method
6.4.2 Computational methods for the network cross K
function methods
6.4.2.1 Computational methods for the network local auto K
function method
6.4.2.3 Computational methods for the network global cross K function method
6.4.2.3 Computational methods for the network global Voronoi
cross K
function method
Chapter 7 Network spatial autocorrelation
7.1 Classification of spatial autocorrelations
7.2 Spatial randomness of the attribute values of network cells
7.2.1 Permutation spatial randomness
7.2.2 Normal variate spatial randomness
7.3 Network Moran’s I statistics
7.3.1 Network local Moran’s I statistic
7.3.2 Network global Moran’s I statistic
7.4 Computational methods for network Moran’s I statistics
Chapter 8 Network point cluster analysis and clumping method
8.1 Network point cluster analysis
8.1.1 General hierarchical point cluster analysis
8.1.2 Hierarchical point clustering methods with specific intercluster distances
8.1.2.1 Network closestpair point clustering method
8.1.2.2Network farthestpair point clustering method
8.1.2.3 Network averagepair point clustering method
8.1.2.4 Network point clustering methods with other interclaster distances
8.2 Network clumping method
8.2.1 Relation to network point cluster analysis
8.2.2 Statistical test with respect to the number of clumps
8.3 Computational methods for network point cluster analysis and clumping method
8.3.1 General computational framework
8.3.2 Computational methods for individual intercluster distances
8.3.2.1 Computational methods for the network closestpair point clustering
method
8.3.2.1 Computational methods for the network farthestpair point clustering
method
8.3.2.3 Computational methods for the network averagepair point
clustering
method
8.3.3 Computational aspects of the network clumping method
Chapter 9 Network point density estimation methods
9.1 Network histograms
9.1.1 Network cell histograms
9.1.2 Network Voronoi cell histograms
9.1.3 Network cellcount method
9.2 Network kernel density estimation methods
9.2.1 Network kernel functions
9.2.2 Equalsplit discontinuous kernel functions
9.2.3 Equalsplit continuous kernel functions
9.3 Computational methods for network point density estimation
9.3.1 Computational methods for network cell histograms with equallength network cells
9.3.2 Computational method for equalsplit discontinuous kernel density functions
9.3.3 Computational method for equalsplit continuous kernel density functions
Chapter 10 Network spatial interpolation
10.1 Network inversedistance weighting
10.1.1 Concepts of neighborhoods on a network
10.1.2 Network inversedistance weighting predictor
10.2 Network kriging
10.2.1 Network kriging models
10.2.2 Concepts of stationary processes on a network
10.2.3 Network variogram models
10.2.4 Network kriging predictors
10.3 Computational methods for network spatial interpolation
10.3.1 Computational methods for network inversedistance weighing
10.3.2 Computational methods for network kriging
Chapter 11 Network Huff model
11.1 Concepts of the network Huff model
11.1.1 Huff models
11.1.2 Dominant market subnetworks
11.1.3 Huffbased demand estimation
11.1.4 Huffbased locational optimization
11.2 Computational methods for the Huffbased demand estimation
11.2.1 Shortestpath tree distance
11.2.2 Choice probabilities in terms of shortestpath tree distances
11.2.3 Analytical formula for the Huffbased demand estimation
11.2.4 Computational tasks and their time complexities for the Huffbased demand estimation
11.3 Computational methods for the Huffbased locational optimization
11.3.1 Demand function for a newly entering store
11.3.2 Topologically invariant shortestpath trees
11.3.3 Topologically invariant link sets
11.3.4 Numerical method for the Huffbased locational optimization
11.3.5 Computational tasks and their time complexities for the Huffbased locational optimization
Chapter 12 GISbased tools for spatial analysis along networks and their application
12.1 Preprocessing tools in SANET
12.1.1 Tool for testing network connectedness
12.1.2 Tool for assigning points to the nearest points on a network
12.1.3 Tool for computing shortestpath distances between points
12.1.4 Tool for generating random points on a network
12.2 Statistical tools in SANET and their applications
12.2.1 Tools for network Voronoi diagrams and their application
12.2.2 Tools for network nearest neighbor distance methods and their application
12.2.2.1 Network global auto nearestneighbor distance method
12.2.2.2 Network global cross nearestneighbor distance method
12.2.3 Tools for network K function methods and their application
12.2.3.1 Network global auto K function method
12.2.3.2 Network global cross K function method
12.2.3.3 Network global Voronoi cross K function method
12.2.3.4 Network local cross K function method
12.2.4 Tools for network cluster analysis and their application
12.2.5 Tools for network kernel density estimation methods and their application
12.2.6 Tools for network spatial interpolation methods and their application
References
Index
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