Point pattern analysis
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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

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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

    events

    -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

area

-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

    region

    -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

    pattern


Distance based point pattern measures1

Distance-Based Point Pattern Measures

  • G function

    -Simplest

    -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

    distribution

    -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 statistically1

Assessing Point Patterns Statistically


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

    distribution

    -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


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