CSIS workshop on Research Agenda for Spatial Analysis Position paper
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Transcript of CSIS workshop on Research Agenda for Spatial Analysis Position paper
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CSIS workshop on Research Agenda for
Spatial Analysis
Position paper
By Atsu Okabe
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The real space is complex, but … Spatial analysts
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Through the glasses of spatial analysts
Assumption 1
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Through the glasses of spatial analysts
Assumption 2
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In spatial point processes,the homogeneous assumption means ….
Uniform density
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Through the glasses of spatial analysts
Assumption 3
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Through the glasses of spatial analysts
Assumption 4
∞
e.g. Poisson point processes
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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
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Advantages
Analytical derivation is tractable
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Advantages
No boundary problem!
http://www.whitecliffscountry.org.uk/gallery/cliffs1.asp
boundary problem
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Actual example
Insects on the White desert, Egypt
http://www.molon.de/galleries/Egypt_Jan01/WhiteDesert/imagehtm/image12.htm
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Actual example
“Scattered village” on Tonami plain, Japan
http://www.sphere.ad.jp/togen/photo-n.html
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Houses on the Tonami plain studied by Matsui
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When it comes to spatial analysis in an urbanized area, …
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The real city is 3D
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The real city consists of many kinds of features
heterogeneous
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We cannot go through buildings!
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The real urban space is bounded by railways, ….
bounded
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The “ideal” space is far from the real space!
Real space “Ideal” space
The objective is to fill this gap
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Convenience stores in Shibuya
constrained by the street network!
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Dangerous to ignore the street network
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Random?
NO!?
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Random?
YES!!
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Misleading
Non-random on a plane Random on a network
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Too unrealistic!
To represent the real space by the “ideal” space
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Alternatively,
Represent the real space by network space
Assumption 1
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Network space is appropriate for traffic accidents
http://www.sanantonio.gov/sapd/TrFatalityMap.htm
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Robbery and Car Jacking
http://www.new-orleans.la.us/cnoweb/nopd/maps/4week/4wkrob.html
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Pipe corrosion
http://www.fugroairborne.com/CaseStudies/pipe_line.jpg
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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.
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Banks, stores and many kinds of facilities are not on streets!
http://www.do-map.net/
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How to use facilities?
home facilities
Through networks
gate EntranceStreet Street
sidewalks
roads
railways
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Facilities are represented by access points on a network
housecamera shop
Access point Access point
StreetStreet
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An example: banks in Shibuya
Banks
are represented
by
access points
(entrances)
on a street network
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Assumption 2
The distance between two points on a network is measured by the shortest-path distance.
Assumption 1
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Euclidean distance vs shortest path distance
Koshizuka and Kobayashi
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Ordinary Voronoi diagram vsManhattan Voronoi diagram
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One-way
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Heterogeneous
A network space is
heterogeneous
in the sense
that
it is not
isotropic.
Assumption 1
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Assumption 3: probabilistically homogeneous
Sounds unrealistic but NOT!
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Density function on a network
f(x)
Probabilistically homogeneous = uniform distribution
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Density function on a network
Traffic density
NOX density
Housing density
Population density
etc.
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Housing density function
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Population density function
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The distribution of stores are affected by the
population density.
The population distribution is not uniform
Probabilistically homogeneous assumption is unrealistic
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Uniform network transformation
Any p-heterogeneous network
can be transformed into
a p-homogeneous network!
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Probability integral transformation
x
xFdxxfy ).()(
Density function on a link: non-uniform distribution
Un
iform d
ist ribu
tion
y
x
f(x)
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Assumption 4: Bounded
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Boundary treatment
Plane: hard
Network: easier
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How to deal with features in 3D space?
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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
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Stores in a 3D spacerepresented byaccess points on a network
Simple!
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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
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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
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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