Ch 5Ch 5Practical Point Pattern AnalysisPractical Point Pattern Analysis

Spatial Stats & Data Analysis

by by Magdaléna DohnalováMagdaléna Dohnalová

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

In fact, what we need to know is..

Where the pattern deviates from expectations

>>> >>> CLUSTER DETECTIONCLUSTER DETECTION

Where are the Clusters?

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

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

GAM…how the heck?@!$#!@

Two dimensional gridSeries 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

Pattern of Circles used by GAM

About Cluster Detectors

More recent genetic algorithms (intelligent)– Map Explorer (MAPEX) & Space Time Attribute

Creature (STAC)Data Availability

– When aggregate data -> MAUPVariation 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

Extension of Basic Point PatternMultiple 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

Extension of Basic Point PatternWhen 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

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!

Point Pattern Analysis: Proximity Polygons

Delaunay proximity polygons

– Distribution of area

– The number of neighbors

– Lengths of Edges

– Minimum Spanning Tree (from Gabriel graph)

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)

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.