csis workshop on research agenda for spatial analysis position paper
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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