CSIS workshop on Research Agenda for

Spatial Analysis

Position paper

By Atsu Okabe

The real space is complex, but … Spatial analysts

Through the glasses of spatial analysts

Assumption 1

Through the glasses of spatial analysts

Assumption 2

In spatial point processes,the homogeneous assumption means ….

Uniform density

Through the glasses of spatial analysts

Assumption 3

Through the glasses of spatial analysts

Assumption 4

∞

e.g. Poisson point processes

Summing up,

In most spatial point pattern analysis, Assumption 1: 2-Dimensional Assumption 2: Homogeneous Assumption 3: Euclidean distance Assumption 4: Unbounded The space characterized by these assumptions

= “ideal” space Useful for developing pure theories

Advantages

Analytical derivation is tractable

Advantages

No boundary problem!

http://www.whitecliffscountry.org.uk/gallery/cliffs1.asp

boundary problem

Actual example

Insects on the White desert, Egypt

http://www.molon.de/galleries/Egypt_Jan01/WhiteDesert/imagehtm/image12.htm

Actual example

“Scattered village” on Tonami plain, Japan

http://www.sphere.ad.jp/togen/photo-n.html

Houses on the Tonami plain studied by Matsui

When it comes to spatial analysis in an urbanized area, …

The real city is 3D

The real city consists of many kinds of features

heterogeneous

We cannot go through buildings!

The real urban space is bounded by railways, ….

bounded

The “ideal” space is far from the real space!

Real space “Ideal” space

The objective is to fill this gap

Convenience stores in Shibuya

constrained by the street network!

Dangerous to ignore the street network

Random?

NO!?

Random?

YES!!

Misleading

Non-random on a plane Random on a network

Too unrealistic!

To represent the real space by the “ideal” space

Alternatively,

Represent the real space by network space

Assumption 1

Network space is appropriate for traffic accidents

http://www.sanantonio.gov/sapd/TrFatalityMap.htm

Robbery and Car Jacking

http://www.new-orleans.la.us/cnoweb/nopd/maps/4week/4wkrob.html

Pipe corrosion

http://www.fugroairborne.com/CaseStudies/pipe_line.jpg

Network space

Network space is appropriate to deal with

traffic accidents

robbery and car jacking

pipe corrosion

traffic lights

etc.

because these events occur on a network.

Banks, stores and many kinds of facilities are not on streets!

http://www.do-map.net/

How to use facilities?

home facilities

Through networks

gate EntranceStreet Street

sidewalks

roads

railways

Facilities are represented by access points on a network

housecamera shop

Access point Access point

StreetStreet

An example: banks in Shibuya

Banks

are represented

by

access points

(entrances)

on a street network

Assumption 2

The distance between two points on a network is measured by the shortest-path distance.

Assumption 1

Euclidean distance vs shortest path distance

Koshizuka and Kobayashi

Ordinary Voronoi diagram vsManhattan Voronoi diagram

One-way

Heterogeneous

A network space is

heterogeneous

in the sense

that

it is not

isotropic.

Assumption 1

Assumption 3: probabilistically homogeneous

Sounds unrealistic but NOT!

Density function on a network

f(x)

Probabilistically homogeneous = uniform distribution

Density function on a network

Traffic density

NOX density

Housing density

Population density

etc.

Housing density function

Population density function

The distribution of stores are affected by the

population density.

The population distribution is not uniform

Probabilistically homogeneous assumption is unrealistic

Uniform network transformation

Any p-heterogeneous network

can be transformed into

a p-homogeneous network!

Probability integral transformation

x

xFdxxfy ).()(

Density function on a link: non-uniform distribution

Un

iform d

ist ribu

tion

y

x

f(x)

Assumption 4: Bounded

Boundary treatment

Plane: hard

Network: easier

How to deal with features in 3D space?

Stores in multistory buildings

A store on the 1st floor

A Store on the 2nd floor

A store on the 3rf floor

Ele

vato

r

Street

Stores in a 3D spacerepresented byaccess points on a network

Simple!

Summing up,

Spatial analysis

on a plane

2-dimensional

Isotropic

Probabilistically homogeneous

Euclidean distance

Unbounded

Spatial analysis

on a network

1-dimensional

Non-isotropic

Probabilistically homogeneous

Shortest-path distance

Bounded

Methods for spatial analysis on a network

Nearest distance methodConditional nearest distance methodCell count methodK-function methodCross K-function methodClumping methodSpatial interpolationSpatial autocorrelation Huff model

SANET: A Toolbox for Spatial Analysis on a NETwork* 　 Network Voronoi diagram*　 K-function method* 　 Cross K-function method* 　 Random points generation (Monte Carlo) Nearest distance method Conditional nearest distance method Cell count method Clumping method Spatial interpolation Spatial Autocorrelation Huff model