1. CSIS workshop on Research Agenda for Spatial Analysis Position paper By Atsu Okabe

2. The real space is complex, but … Spatial analysts

3. Through the glasses of spatial analysts Assumption 1

4. Through the glasses of spatial analysts Assumption 2

5. In spatial point processes, the homogeneous assumption means …. Uniform density

6. Through the glasses of spatial analysts Assumption 3

7. Through the glasses of spatial analysts Assumption 4 ∞ e.g. Poisson point processes

8. 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

9. Advantages Analytical derivation is tractable

10. Advantages No boundary problem! http://www.whitecliffscountry.org.uk/gallery/cliffs1.asp boundary problem

11. Actual example Insects on the White desert, Egypt http://www.molon.de/galleries/Egypt_Jan01/WhiteDesert/imagehtm/image12.htm

12. Actual example “Scattered village” on Tonami plain, Japan http://www.sphere.ad.jp/togen/photo-n.html

13. Houses on the Tonami plain studied by Matsui

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

15. The real city is 3D

16. The real city consists of many kinds of features heterogeneous

17. We cannot go through buildings!

18. The real urban space is bounded by railways, …. bounded

19. The “ideal” space is far from the real space! Real space “Ideal” space The objective is to fill this gap

20. Convenience stores in Shibuya constrained by the street network!

21. Dangerous to ignore the street network

22. Random? NO!?

23. Random? YES!!

24. Misleading Non-random on a plane Random on a network

25. Too unrealistic! To represent the real space by the “ideal” space

26. Alternatively, Represent the real space by network space Assumption 1

27. Network space is appropriate for traffic accidents http://www.sanantonio.gov/sapd/TrFatalityMap.htm

28. Robbery and Car Jacking http://www.new-orleans.la.us/cnoweb/nopd/maps/4week/4wkrob.html

29. Pipe corrosion http://www.fugroairborne.com/CaseStudies/pipe_line.jpg

30. 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.

31. Banks, stores and many kinds of facilities are not on streets! http://www.do-map.net/

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

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

34. An example: banks in Shibuya Banks are represented by access points (entrances) on a street network

35. Assumption 2 The distance between two points on a network is measured by the shortest-path distance. Assumption 1

36. Euclidean distance vs shortest path distance Koshizuka and Kobayashi

37. Ordinary Voronoi diagram vs Manhattan Voronoi diagram

38. One-way

39. Heterogeneous A network space is heterogeneous in the sense that it is not isotropic. Assumption 1

40. Assumption 3: probabilistically homogeneous Sounds unrealistic but NOT!

41. Density function on a network f(x)f(x) Probabilistically homogeneous = uniform distribution

42. Density function on a network Traffic density NOX density Housing density Population density etc.

43. Housing density function

44. Population density function

45. The distribution of stores are affected by the population density. The population distribution is not uniform Probabilistically homogeneous assumption is unrealistic

46. Uniform network transformation Any p-heterogeneous network can be transformed into a p-homogeneous network!

47. Probability integral transformation Density function on a link: non-uniform distribution Uniform distribution y x f(x)

48. Assumption 4: Bounded

49. Boundary treatment Plane: hard Network: easier

50. How to deal with features in 3D space?

51. 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

52. Stores in a 3D space represented by access points on a network Simple!

53. 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

54. 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

55. 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