CSIS workshop on Research Agenda for Spatial Analysis
- Slides: 55
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! m e l b o r yp r a d n bou http: //www. whitecliffscountry. org. uk/gallery/cliffs 1. asp
Actual example Insects on the White desert, Egypt http: //www. molon. de/galleries/Egypt_Jan 01/White. Desert/imagehtm/image 12. 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 3 D
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/Tr. Fatality. Map. htm
Robbery and Car Jacking http: //www. new-orleans. la. us/cnoweb/nopd/maps/4 week/4 wkrob. html
Pipe corrosion http: //www. fugroairborne. com/Case. Studies/pipe_line. jpg
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 sidewalks facilities roads gate Street Entrance Street railways Through networks
Facilities are represented by access points on a network camera shop house Street Access point
An example: banks in Shibuya Banks are represented by access points (entrances) on a street network
Assumption 1 Assumption 2 The distance between two points on a network is measured by the shortest-path distance.
Euclidean distance vs shortest path distance Koshizuka and Kobayashi
Ordinary Voronoi diagram vs Manhattan Voronoi diagram
One-way
Assumption 1 Heterogeneous A network space is heterogeneous in the sense that it is not isotropic.
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
Probabilistically homogeneous assumption is unrealistic The distribution of stores are affected by the population density. The population distribution is not uniform
Uniform network transformation Any p-heterogeneous network can be transformed into a p-homogeneous network!
Probability integral transformation y Uniform distribution f(x) x Density function on a link: non-uniform distribution
Assumption 4: Bounded
Boundary treatment Plane: hard Network: easier
How to deal with features in 3 D space?
Stores in multistory buildings Elevator A store on the 3 rf floor A Store on the 2 nd floor A store on the 1 st floor Street
Stores in a 3 D 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
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