1. Ch 5Practical Point Pattern Analysis Spatial Stats & Data Analysis by Magdaléna Dohnalová

2. Problems of pure Spatial Statistical Analysis • Null Hypothesis: Is that IRP/CSR? • Insufficient description • First-order influence • Process-Pattern Matching • Either it does or it doesn’t • Global technique

3. In fact, what we need to know is.. • Where the pattern deviates from expectations >>> CLUSTER DETECTION • Where are the Clusters?

4. Case Study:Sellafield Leukemia Study, UK • Children leukemia deaths clustered around nuclear plant • Proved that THERE WAS a cluster, but missing evidence of linking cause • Apparent clusters occur naturally in many diseases • The actual number in cluster was very low • Similar clusters have been found around nonnuclear plants

5. Cluster analysis of Point Patterns • Problem with small clusters • Distance Rings • Rates of occurrence • Distance form the plant • Geographical Analysis Machine (GAM) • Automated cluster detector for point patterns

6. GAM…how the heck?@!$#!@ • Two dimensional grid • Series of different circles • various size and density • Number of events within each circle • Exceeds threshold? (Monte Carlo simulation of expected pattern) • If YES, draw circle on the map • END RESULT: map of significant circles

7. Pattern of Circles used by GAM

8. About Cluster Detectors • More recent genetic algorithms(intelligent) • Map Explorer (MAPEX) & Space Time Attribute Creature (STAC) • Data Availability • When aggregate data -> MAUP • Variation in Background Rate • Assume uniform geography • Overlapping of significant circles • not independent • Setting variable threshold!!! • Time problem • Snapshot effect • Aggregation over time, similar to MAUP

9. Extension of Basic Point Pattern • Multiple Sets of Events • Contingency table analysis • Chi-Square Test • Discards location information • Cross Functions (G and K functions) • Cumulative Nearest-Neighbor function • Distance from event in each pattern (G) • Events counts within in distance to the other (K) • Random if events are independent of each other

10. Extension of Basic Point Pattern • When was it Clustered? • Clustering in space and time together! • Knox test • Distance in space (near-far) and time (close-distant) • Contingency table + Chi-square • Threshold decision – similar to MAUP • Mantel Test • Distance and space distance for all objects • Modified K function • Combining two K functions in Contingency table • Test difference between the two

11. Point Pattern Analysis: Proximity Polygons • Using DENSITY and DISTANCE • Geographical Space is not random! • Delaunay triangulation of proximity polygons • Neighborhood relations are defined in respect to local patterns!

12. Point Pattern Analysis: Proximity Polygons • Delaunay proximity polygons • Distribution of area • The number of neighbors • Lengths of Edges • Minimum Spanning Tree (from Gabriel graph)

13. Point Pattern Analysis: Distance Based Methods • Distance Matrices • Large amount of data (not the most efficient but convenient for computer calculations) • Underlines shortest distance (nearest neighbor & G function) • Convert to Adjacency Matrices (K function) • Derived Matrices (F function)

14. Questions • What are the two major questions we ask about clusters? • What is the final product of GAM? • What are the main challenges in cluster detection? • What are the strengths of using Proximity Polygons for cluster detection? Describe the minimum spanning tree.