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Point Pattern Analysis. Chapter 4 Geographic Information Analysis By David O’ Sullivan and David J. Unwin. Introduction to Point Pattern Analysis. Simplest Possible Spatial Data -A point pattern is a set of events in a study region -Each event is symbolized by a point object

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point pattern analysis

Point Pattern Analysis

Chapter 4

Geographic Information Analysis

By David O’ Sullivan and David J. Unwin

introduction to point pattern analysis
Introduction to Point Pattern Analysis
  • Simplest Possible Spatial Data

-A point pattern is a set of events in a study region

-Each event is symbolized by a point object

-Data are the locations of a set of point objects

  • Applications

-Hot-spot analysis (crime, disease)

-Vegetation, archaeological studies

introduction to point pattern analysis1
Introduction to Point Pattern Analysis
  • Requirements for a set of events to constitute a point pattern

-Pattern should be mapped on a plane

-Study area determined objectively

-Pattern is a census of the entities of interest

-One-to-one correspondence between objects and


-Event locations are proper

introduction to point pattern analysis2
Point Density

-First-order effect: Variation

of intensity of a process

across space

-Number of events per unit


-Absolute location

Point Separation

-Second-order effect:

Interaction between

locations based on distance

between them

-Relative location

Introduction to Point Pattern Analysis
  • Describing a point pattern
introduction to point pattern analysis3
Introduction to Point Pattern Analysis
  • Descriptive statistics to provide summary descriptions of point patterns

-Mean center

-Standard Distance

density based point pattern measures
Density-Based Point Pattern Measures
  • First-order effect
  • Sensitive to the definition of the study area
density based point pattern measures1
Density-Based Point Pattern Measures
  • Quadrant count methods

-Record number of events of a pattern in a set of

cells of a fixed size

-Census vs. Random

density based point pattern measures2
Density-Based Point Pattern Measures
  • Kernel-density estimation

-Pattern has a density at any location in the study


-Good for hot-spot analysis, checking first-order

stationary process, and linking point objects to

other geographic data

Naive method

distance based point pattern measures
Distance-Based Point Pattern Measures
  • Second-order effect
  • Nearest-neighbor distance

-The distance from an event to the nearest event in

the point pattern

  • Mean nearest-neighbor distance

-Summarizes all the nearest-neighbor distances by a

single mean value

-Throws away much of the information about the


distance based point pattern measures1
Distance-Based Point Pattern Measures
  • G function


-Examines the cumulative frequency distribution of

the nearest-neighbor distances

-The value of G for any distance tells you what

fraction of all the nearest-neighbor distances in the

pattern are less than that distance

distance based point pattern measures2
Distance-Based Point Pattern Measures
  • F function

-Point locations are selected at random in the study

region and minimum distance from point location to

event is determined

-The F function is the cumulative frequency


-Advantage over G function: Increased sample size

for smoother curve

distance based point pattern measures3
Distance-Based Point Pattern Measures
  • K function

-Based on all distances between events

-Provides the most information about the pattern

distance based point pattern measures4
Distance-Based Point Pattern Measures
  • Problem with all distance functions are edge effects
  • Solution is to implement a guard zone
assessing point patterns statistically
Assessing Point Patterns Statistically
  • Null hypothesis

-A particular spatial process produced the observed

pattern (IRP/CSR)

  • Sample

-A set of spatial data from the set of all possible

realizations of the hypothesized process

  • Testing

-Using a test to illustrate how probable an observed

value of a pattern is relative to the distribution of values

in a sampling distribution

assessing point patterns statistically2
Assessing Point Patterns Statistically
  • Quadrant counts

-Probability distribution for a quadrant count

description of a point pattern is given by a Poisson


-Null hypothesis: (IRP/CSR)

-Test statistic: Intensity (λ)

-Tests: Variance/mean ratio, Chi-square

  • Nearest-neighbor distances

-R statistic

assessing point patterns statistically3
Assessing Point Patterns Statistically
  • G and F functions

-Plot observed pattern and IRP/CSR pattern

assessing point patterns statistically4
Assessing Point Patterns Statistically
  • K function

-Difficult to see small differences between expected

and observed patterns when plotted

-Develop another function L(d) that should equal

zero if K(d) is IRP/CSR

-Use computer simulations to generate IRP/CSR

(Monte Carlo procedure)

critiques of spatial statistical analysis
Critiques of Spatial Statistical Analysis
  • Peter Gould

-Geographical data sets are not samples

-Geographical data are not random

-Geographical data are not independent random

-n is always large so results are almost always

statistically significant

-A null hypothesis of IRP/CSR being rejected means

any other process is the alternative hypothesis

  • David Harvey

-Altering parameter estimates by changing study

region size often can alter conclusions