Spatial Analysis Along Networks E-Book

Atsuyuki Okabe

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Statistics in Practice
• Sprache: Englisch

Seitenzahl: 544

Veröffentlichungsjahr: 2012

Beschreibung

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.

Leseprobe

Cover

Statistics in Practice

Title Page

Copyright

Preface

Acknowledgements

Chapter 1: Introduction

1.1 What is Network Spatial Analysis?

1.2 Review of Studies of Network Events

1.3 Outline of the Book

Chapter 2: Modeling Spatial Events on and Alongside Networks

2.1 Modeling the Real World

2.2 Modeling Networks

2.3 Modeling Entities on Network Space

2.4 Stochastic Processes on Network Space

Chapter 3: Basic Computational Methods for Network Spatial Analysis

3.1 Data Structures for One-Layer Networks

3.2 Data Structures for Nonplanar Networks

3.3 Basic Geometric Computations

3.4 Basic Computational Methods on Networks

Chapter 4: Network Voronoi Diagrams

4.1 Ordinary Network Voronoi Diagram

4.2 Generalized Network Voronoi Diagrams

4.3 Computational Methods for Network Voronoi Diagrams

Chapter 5: Network Nearest-Neighbor Distance Methods

5.1 Network Auto Nearest-Neighbor Distance Methods

5.2 Network Cross Nearest-Neighbor Distance Methods

5.3 Network Nearest-Neighbor Distance Method for Lines

5.4 Computational Methods for the Network Nearest-Neighbor Distance Methods

Chapter 6: Network K Function Methods

6.1 Network Auto K Function Methods

6.2 Network Cross K Function Methods

6.3 Network K Function Methods in Relation to Geometric Characteristics of a Network

6.4 Computational Methods for the Network K Function Methods

Chapter 7: Network Spatial Autocorrelation

7.1 Classification of Autocorrelations

7.2 Spatial Randomness of the Attribute Values of Network Cells

7.3 Network Moran's I statistics

7.4 Computational Methods for Moran's I Statistics

Chapter 8: Network Point Cluster Analysis and Clumping Method

8.1 Network Point Cluster Analysis

8.2 Network Clumping Method

8.3 Computational Methods for the Network Point Cluster Analysis and Clumping Method

Chapter 9: Network Point Density Estimation Methods

9.1 Network Histograms

9.2 Network Kernel Density Estimation Methods

9.3 Computational Methods for Network Point Density Estimation

Chapter 10: Network Spatial Interpolation

10.1 Network Inverse-Distance Weighting

10.2 Network Kriging

10.3 Computational Methods for Network Spatial Interpolation

Chapter 11: Network Huff Model

11.1 Concepts of the Network Huff Model

11.2 Computational Methods for the Huff-Based Demand Estimation

11.3 Computational Methods for the Huff-Based Locational Optimization

Chapter 12: GIS-Based Tools for Spatial Analysis Along Networks and Their Application

12.1 Preprocessing Tools in SANET

12.2 Statistical Tools in SANET and Their Application

References

Index

Statistics in Practice

Series Advisors

Human and Biological Sciences

Stephen Senn

CRP-Santé, Luxembourg

Earth and Environmental Sciences

Marian Scott

University of Glasgow, UK

Industry, Commerce and Finance

Wolfgang Jank

University of Maryland, USA

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This edition first published 2012

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Library of Congress Cataloging-in-Publication Data

Okabe, Atsuyuki, 1945-

Spatial analysis along networks : statistical and computational methods / Atsuyuki Okabe and Kokichi Sugihara.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-77081-8 (cloth)

1. Spatial analysis (Statistics) 2. Spatial analysis (Statistics)–Data processing. 3. Geography–Network analysis. I. Sugihara, Kokichi, 1948- II. Title.

QA278.2.O359 2011

519.5′36–dc23

2011040047

A catalogue record for this book is available from the British Library.

ISBN: 978-0-470-77081-8

Preface

As its title indicates, this book is devoted to spatial analysis along networks, referred to as network spatial analysis, or more explicitly, statistical and computational methods for analyzing events occurring on and alongside networks. Network spatial analysis is of practical use for analyzing, among other things, the occurrence of traffic accidents on highways, the incidence of crime on streets, the location of stores alongside roads, and the contamination of rivers (Chapter 1 introduces many applications). This usefulness is the main reason we focus on network spatial analysis in this volume. However, there is also a more general and somewhat more ambitious justification for this work. That is, when viewed from a broader perspective, we expect that network spatial analysis will prove to be a first step toward next-generation spatial analysis.

Having reviewed the extant literature on spatial analysis, we note that most empirical studies incorporate spatially aggregated data across subareas, such as administrative districts, census tracts, and postal zones. We refer to this type of spatial analysis as subarea-based spatial analysis or meso-scale spatial analysis. One of the earliest and most notable examples of this type of spatial analysis is included in a compilation titled The City (Park, Burgess, and McKenzie, 1925), written by sociologists at the Chicago School (sometimes described as the Ecological School). More specifically, Burgess (1925) surveyed land use of subareas in Chicago and formulated the concentric-zone model, subsequently followed by Hoyt's (1939) sector model and the Harris–Ullman multiple nuclei model (Harris and Ullman, 1945).

Since then, subarea-based spatial analysis has become one of the most important approaches to empirical spatial analysis. Even today, we frequently employ subarea-based spatial analysis for empirical studies because subarea data, including population and other census-related data, are widely available and because it is generally straightforward to apply ordinary statistical techniques, including regression analysis, to the attribute values of subareas. Unlike the empirical literature, we find that the development of most theoretical work on spatial analysis has assumed an ‘ideal space’, that is, real space is represented by unbounded homogeneous space with Euclidean distance. This ideal space is convenient for developing pure theories of spatial analysis or spatial stochastic processes; indeed, the derivations of many useful theorems employ this assumption (see, e.g., Illian et al., (2008)). However, ideal space is far from the real world.

In the late twentieth century, the availability of detailed spatial data increased dramatically thanks to rapid progress in data acquisition technologies, such as the global positioning system (GPS) and many kinds of geosensors. Better data availability potentially enables us to analyze spatial events in detail by representing individual entities in the real world in terms of geometric objects in two- or three-dimensional Cartesian space instead of aggregating them into subareas (see Chapter 2 for this representation). We describe this possible form of spatial analysis as object-based spatial analysis or micro-scale spatial analysis, in contrast to the well-established subarea-based spatial analysis or meso-scale spatial analysis. At present, however, the methods for micro-scale spatial analysis are at an early stage. We believe that one clue to micro-scale spatial analysis would be to represent real space by networks embedded in two- or three-dimensional Cartesian space. This is because many kinds of events or activities in the real world are constrained by networks, such as streets, railways, water and gas pipe lines, rivers, electric wires, and communication networks. A first step toward micro-spatial analysis would thus appear to be network-constrained spatial analysis, which is the main concern of this volume.

In network spatial analysis, we measure the shortest-path distance. Unfortunately, its computation is much more difficult than that of Euclidean distance because it requires the management of network topology. Therefore, network spatial analysis becomes practical only when efficient computational methods are available. Dijkstra (1959) developed a key algorithm for this purpose in the middle of last century. Since then, there has been extensive study of location problems on networks by a variety of researchers, mainly in operations research (Handler and Mirchandani, 1979; Daskin, 1995; for a review, see Labbe, Peeters, and Thisse (1995)). We should note that the focus in these studies has been locational optimization or the computing of network characteristics (e.g., Kansky, 1963; Haggett and Chorley, 1969), with rather less attention paid to the statistical analysis of events on networks.

To fill this gap in the literature, we develop statistical and computational methods for network spatial analysis by introducing computational methods originally developed for operations research and computational geometry (Preparata and Shamos, 1985; Chapter 3 in this volume presents some basic computational methods). In this sense, the network spatial analysis presented in this volume is a first step toward micro-scale spatial analysis. However, we cannot present real world space by either network or Euclidean space alone as it is a complex hybrid system with elements of both. The next step, then, would be object-based spatial analysis in a hybrid space consisting of a discrete network space with shortest-path distance and a continuous space with Euclidean, or more generally, geodesic distance. An initial attempt is Cressie et al. (2006).

We are now in the midst of an ongoing revolution brought about by information and communication technologies. In the future, microcomputer tips, tags, and geosensors will be embedded in almost every entity (including moving objects) in our environment, and the integration of these devices with communication systems (e.g., the Internet) will establish an intellectual system joining the virtual world of computers and the global real world. This system will then realize a society we refer to as the ubiquitous computing society, in which at any time and in any place, people can receive the most appropriate personalized information for action given their particular circumstances in time and space (Sakamura and Koshizuka, 2005). To construct this system, micro-scale spatial analysis is expected to extend to real-time spatial analysis, that is, spatial analysis in which the circumstances of an acting body (including a person, a group of persons, a company, or possibly a robot) are analyzed and appropriate personalized information for action is derived almost instantaneously (Okabe, 2009a, 2009b). We intend that this volume, in presenting state-of-the-art methodology for network spatial analysis, will contribute a first step toward micro-scale spatial analysis and encourage our readers to further develop micro-scale spatial analysis and, from there, tackle the challenge of real-time spatial analysis.

Atsuyuki OkabeKokichi SugiharaMarch 2012

Acknowledgements

When we first thought of the concept underlying this book in June 2007, we consulted Noel Cressie on possible publication. In turn, he was kind enough to introduce our proposal to the statistics and mathematics section at John Wiley. A positive response meant that our long project could begin in September 2007. Since then, so very many people have helped us in different ways in developing and presenting this book that it would be impossible to acknowledge all of them individually.

To start with, we are very grateful to those who have read our drafts and offered useful comments, particularly Ikuho Yamada on the general concepts underpinning network spatial analysis (Chapters 1 and 2) and spatial autocorrelation (Chapter 8), Toshiaki Satoh on kernel density estimation (Chapter 9) and GIS-based tools (Chapter 12), and Kei-ichi Okunuki on the Huff model (Chapter 11). Our special thanks also go to those with whom we discussed related subjects and who in turn provided us with inspiration. These especially include Mike Tiefelsdorf and Barry Boots on spatial autocorrelation, Yuzo Maruyama and Yonghe Li on kriging, Shino Shiode on inverse-distance weighting and cell counting, and Hisamoto Hiyoshi on spatial interpolation. They also include Atsuo Suzuki, Takehiro Furuta, and Shinji Imahori on equal cell splitting, Kei-ichi Okunuki and Masatoshi Morita on the K function method, and Yasushi Asami and Yukio Sadahiro on urban analysis.

We would also like to express our thanks to those who helped us to run the necessary programs, particularly Toshiaki Satoh, Kayo Okabe, Akiko Takahashi, and the staff at the Center for Spatial Information Science (CSIS) at the University of Tokyo and the Information Science Research Center at Aoyama Gakuin University. We are also indebted to Ayako Teranishi for collecting the more than 500 related papers, entering them in our database, and editing the references and compiling the index, and to Tsukasa Takenaka for constructing the online database with which we could develop our book while we were away. We also thank Masako Yoshida for the retrieval program used for the references, Tetsuo Kobayashi for collecting research articles, and Aya Okabe for designing the website, along with the web crew members involved in its management at CSIS, through which we received many practical comments on the GIS-based toolbox known as SANET from users across 51 countries.

We are thankful to the staff at John Wiley, particularly Richard Davies, Ilaria Meliconi, Heather Kay, Susan Barclay, Kathryn Sharples, and Prachi Sinha Sahay for their helpful assistance. We also acknowledge a grant-in-aid by the Japan Society for the Promotion of Science for a project entitled ‘Development of methods, algorithms, and GIS-based tools for statistical spatial analysis on networks’ (#20300098), and data provision by the Chiba Prefectural Police, NTT Data, and CSIS. Finally, we thank our respective partners, Kayo Okabe and Keiko Sugihara, for their lifelong encouragement and invaluable support before and during the writing of this book.

Chapter 1

Introduction

This book presents statistical and computational methods for analyzing events that occur on or alongside networks. To this end, the first three chapters are concerned with preparations. This chapter shows the scope of this book, Chapter 2 fixes a general framework for spatial analysis, and Chapter 3 describes computational methods commonly used throughout the subsequent chapters. In this introductory chapter, we first describe the events under consideration, i.e., events that occur on and alongside networks, termed network events. Second, we show that if traditional spatial analysis assuming a plane with Euclidean distances, referred to as planar spatial analysis, is applied to network events, then it is likely to lead to false conclusions. Third, to overcome this shortcoming, we propose a new type of spatial analysis, namely network spatial analysis, which assumes a network with shortest-path distances. Fourth, we review studies on network events in the related literature and show how to apply network spatial analysis to those studies. Last, we describe the structure of the twelve chapters of the book and suggest how to read them according to the reader's interests. Note that network spatial analysis viewed from a board perspective is described in the preface of this volume.

1.1 What is Network Spatial Analysis?

To introduce this new type of spatial analysis, we first define a key concept, network events, and next consider typical questions about network events to be solved by network spatial analysis. We then describe the salient features of network spatial analysis in contrast to the traditional planar spatial analysis.

1.1.1 Network Events: Events on and Alongside Networks

In the real world, there are numerous and various events that are strongly constrained by networks, such as car crashes on roads and fast-food shops located alongside streets. We call them network-constrained events (Yamada and Thill, 2007) or network events for short. Network events can be classified into two classes: events that occur directly on a network (e.g., car crashes on a road), and events that occur alongside a network rather than directly on it (e.g., fast-food shops located alongside a street). We refer to the former as on-network events and the latter as alongside-network events. Consequently, network events consist of on-network events and alongside-network events (Figure 1.1). Note that we sometimes use ‘along’ for both ‘on’ and ‘alongside.'

Figure 1.1 Network (constrained) events consisting of on-network events and alongside-network events.

Figure 1.2 illustrates an actual example of on-network events, where each dot represents a traffic accident around Chiba station, Japan. As with this example, many types of network event have been reported in the related literature, including pedestrian and motor vehicle street accidents, roadkills of animals on forest roads, street crime sites, tree spacing along the roadside, seabirds located along a coastline, beaver lodges in watercourses, levee crevasse distribution on river banks, leakages in gas and oil pipelines, breaks in a wiring network, disconnections on the Internet, and blood clots in a vascular network (studies on network events including these examples will be reviewed in Section 1.2).

Figure 1.2 Sites of traffic accidents around Chiba station, Japan (private roads are not shown).

Figure 1.3 depicts an actual example of alongside-network events, where the black dots indicate advertisement agency sites alongside streets in Shibuya ward, one of the subcentral districts in Tokyo. There are many facilities that are located alongside street networks within densely inhabited areas. In fact, the entrances to almost all facilities in a city are adjacent to streets and users access amenities through these (Figure 1.1). Consequently, the locations of almost all facilities within an urbanized area can be regarded as alongside-network events.

Figure 1.3 The distribution of advertisement agency sites (the black points) alongside streets (the gray line segments) in Shibuya ward, one of the subcentral districts in Tokyo.

On- and alongside-network events such as those in the above examples are the major concern of this book. More specifically, this book primarily focuses on spatial distributions and relationships of such events on and alongside networks. Typical questions to be discussed in this volume are as follows:

Q1: How can we obtain the catchment areas of parking lots in a downtown area including one-way streets, assuming that drivers access their nearest parking lots?

Q2: Do boutiques tend to stand side-by-side alongside streets in a downtown area?

Q3: Do street burglaries tend to take place near railway stations?

Q4: Is the roadside land price of a street segment similar to those of the adjacent street segments?

Q5: How can we locate clusters of fashionable boutiques alongside downtown streets?

Q6: How can we estimate the density of traffic accidents and street crimes incidence, and how can we identify locations where the densities of those occurrence are high, referred to as black spots and hot spots?

Q7: How can we spatially interpolate an unknown NOx (nitrogen oxides) density at an arbitrary point on a road using known NOx densities at observation points in a high-rise building district, such as Midtown Manhattan?

Q8: How can we estimate the probability of a consumer choosing a specific fast-food shop among alternative shops located alongside streets in a downtown area?

1.1.2 Planar Spatial Analysis and its Limitations

To answer the above types of question, we might conventionally use spatial methods that assume:

AP1: Events occur on a continuous (unbounded) plane.

AP2: If a method for analyzing the events includes distance variables, the distances are measured by Euclidean distance.

These types of spatial approach are referred to as planar spatial methods, and analyses made in this way are termed planar spatial analyses. Originally, planar spatial methods were designed for analyzing events on a plane, but in practice, as a matter of convenience, planar spatial methods are often applied to network events. However, this use is likely to lead to false conclusions, which are clearly demonstrated in .