1. IS415 Geospatial Analytics for Business Intelligence Lesson 10: Geospatial Data Analysis- Point Patterns Analysis

2. 2 What will you learn from this lesson The differences between GIS analysis and geospatial data analysis Challenges face in analysing geospatial data The basic concepts of point patterns and point patterns analysis techniques

3. Core Competencies Capable to apply appropriate spatial point analysis techniques to gain insights Capable to provide accurate interpretation of spatial point analysis results 3

4. 4 Background of the study Shanghai retail (tobacco) audit study –Account classification –Total market volume –Volume across key price points and channels –Individual brand profiles

5. 5 The study area CHANGNING DISTRICT LUWAN DISTRICT ZHABEI DISTRICT XUHUI DISTRICT PUDONG NEW AREA HUANGPU DISTRICT YANGPU AREA PUTUO DISTRICT

6. 6 Sales by channel Mom & Pop outlets account for 58% of total sales volume. The average sales per Mom & Pop is much lower than Supermarkets, Hypermarkets and Convenience stores. 16% of the market is made up of brands priced less than 3RMB. 11% of this volume is generated by Mom & Pops. Supermarkets are the second most important channel with 15% of total sales being generated through this channel. Convenience stores generate 13% of total sales while tobacconists are a the fourth most important channel

7. 7 Questions: Where are the locations of the different channel stores? Are these channel stores tend to cluster together or they are evenly distributed? Where are the locations of the top 10% channel stores? Are the locations of the top 10% channel stores even distributed spatially? Is there any association between the distribution of the top 10% channel stores and the distribution of the offices

8. 8 The evil of pin mapping!

9. 9 Thematic map

10. 10 GIS crime!

11. 11 Spatial point pattern analysis methods Kernel density estimation Ripley’s K function L function D function K.hat 12 function

12. 12 Kernel density estimation (Silverman 1986) A method to compute the intensity of a point distribution The general formula: Graphically:

13. 13 Kernel density estimation: simple computation

14. 14 The kernel functions Normal distribution, quartic, triangular

15. 15 KDE: Stores surveyed

16. 16 Thematic map: Stores surveyed

17. 17 KDE: 24hr Convenience store

18. 18 KDE: SME supermarket

19. 19 KDE: Mama/Papa store

20. 20 KDE: Grocery shop

21. 21 KDE: Top 10%

22. 22 The Ripley’s K function (Ripley, 1981) A method to estimate the second-order properties of a point process

23. 23 The L function (Besag 1977) In practice, K function will be normalised to obtained a benchmark of zero L(r)>0 indicates that the observed distribution is geographically concentrated L(r)<0 implies dispersion L(r)=0 indicates complete spatial randomness (CRS)

24. 24 Monte Carlo simulation test of CSR Perform m independent simulation of n events (i.e. 999) in the study region. For each simulated point pattern, estimate K(d) and use the maximum and minimum of these functions for the simulated patterns to define an upper and lower simulation envelope. If the estimated K(d) lies above the upper envelope or below the lower envelope, the estimated K(d) is statistically significant

25. 25 L.hat: 24hr Convenience store

26. 26 L.hat: SME supermarket

27. 27 L.hat: Mama/Papa store

28. 28 L.hat: Grocery shop

29. 29 L.hat: Grocery shop

30. 30 Question: Is the observed pattern of one set of event just a random subset of the overall pattern of a set of combined point patterns?

31. 31 D function (Diggle & Chetwynd 1991) Assuming heterogeneity of the distribution The significant of D(r) can be testing by performing Monte Carlo simulation

32. 32 D function: 24hr convenience store

33. 33 D function: SME supermarket

34. 34 D function: Mama/Papa Store

35. 35 D function: Grocery shop

36. 36 Point map: Top 10% vs all stores

37. 37 D function: Top10%

38. 38 Point map: Top 10% store with sales GT 9RM vs all store

39. 39 D function: Top 10% store with sales GT 9RM

40. 40 Bivariate point process Is the spatial distribution of top10% store independent of the distribution of office locations?

41. 41 Bivariate K function The general formula: The significance of the estimated K.hat 12 can be testing using Monte Carlo simulation

42. 42 K.hat 12 : Top10 vs office

43. 43 SPA (Spatial Point Pattern Analysis) A collection of spatial point pattern analysis functions available within a GIS environment Tight (shared) coupling Data GIS R R Library COM Server

44. 44 Sample code: splancs – Kernel density

45. 45 Sample interface: splancs - Kernel Density Kernel density (kernel2d) K-function (Khat, KenvCsr, KenvLael and KenvTor) L-function (Lhat, LenvCsr, LenvTor) D-function K.hat 12

46. Useful Spatial Point Data Analysis Tools Spatstat: An R library for spatial statistics (http://www.spatstat.org/spatstat/)http://www.spatstat.org/spatstat/ CrimeStat: A Spatial Statistics Program for the Analysis of Crime Incident Locations (http://www.icpsr.umich.edu/CrimeStat/)http://www.icpsr.umich.edu/CrimeStat/ SaTScan™ : a free software that analyzes spatial, temporal and space-time data using the spatial, temporal, or space-time scan statistics. (http://www.satscan.org/)http://www.satscan.org/ 46