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! boundary problem

Actual example Insects on the White desert, Egypt

Actual example “Scattered village” on Tonami plain, Japan

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

Robbery and Car Jacking

Pipe corrosion

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!

How to use facilities? home facilities Through networks gate Entrance Street sidewalks roads railways

Facilities are represented by access points on a network house camera shop Access point Street

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 vs Manhattan 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)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 Density function on a link: non-uniform distribution Uniform distribution 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 1 st floor A Store on the 2 nd floor A store on the 3rf floor Elevator Street

Stores in a 3D space represented by access 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 method Conditional nearest distance method Cell count method K-function method Cross K-function method Clumping method Spatial interpolation Spatial 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