The Nature of Geographic Data

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The Nature of Geographic Data
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Objectives

• Learn about spatial autocorrelation
• Understand relationship between scale and level
  of geographic detail
• How principles of building representation around
  geographic samples are applied
• Learn about smoothness and continuous variation
  and fractals

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Outline

• Introduction
• Fundamental problem revisited
• Spatial autocorrelation and scale
• Spatial sampling
• Spatial interpolation
• Measuring distance effects as spatial
  autocorrelation
• Establishing Dependence in space
• Taming Geographic Geographic Monsters
• Induction and deduction

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1. Introduction

• Space and time are important variables geographic
  analysis
• Decisions in geographic space are based on past
  pattern of behavior
• Some geographic phenomena vary smoothly across
  scale while some show extreme irregularity
• Smoothness and irregularity are most
  distinguishing characteristics of geographic data

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Geographic entity
Geographic Data
Non-spatial (Attributes)
Spatial
Geometric
Nominal Ordinal Interval Ratio Cyclic
Points Lines Polygons
Sampling
Discrete
Fields
Uncertainty
Raster
Vector
Data representation, Attribute Structure,
Georefereincing
Interpolation
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2. The Fundamental Problem Revisited

• Everything is related to everything else but near
  things are more closely related (spatial
  autocorrelation). Without such property
  representation would be difficult. But can also
  negate the validity of many of the conventional
  events
• Consecutive events in time are formalized as
  temporal autocorrelation
• In time we look back at past but in space we must
  look in all directions simultaneously
• Scale or level of detail is the most important
  factor in understanding spatial autocorrelation

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3. Spatial autocorrelation and Scale

• Attribute data are classified as nominal,
  ordinal, interval, ratio and cyclic
• Occurrences as absolute and patterns as
  artificial objects
• Location descriptors are point, line, area,
  surface, time
• Spatial autocorrelation refers to how a variable
  correlates with itself in space
• Features similar in location and attribute are
  said to exhibit positive autocorrelation
• Features similar in location but dissimilar in
  attributes are said to exhibit negative
  autocorrelation.
• Zero autocorrelation when attributes are
  independent of location.

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Spatial Sampling

• Sampling scheme determines the quality of data
  representation
• Sampling types simple random, systematic,
  systematic with random allocation, systematic
  with grid spacing, clustered, transect and
  contour sampling
• Heterogeneous phenomena require large samples to
  capture variability in attributes

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Spatial interpolation

• Purpose of interpolation how to represent gap
  between representation
• Informed judgment based on known functions
• Functions can be
• Linear, oil spill effects vs distance, aircraft
  noise vs distance, visitors vs distance from
  national park
• negative power distance Decline in population
  density from historic areas
• and Negative exponential distance decline in
  retail store patronage with distance
• Isopleth ( Fields measured in ratio or interval
  See box 5.4) and chloropleth maps ( spatially
  intensive)

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Spatial Autocorrelation

• Spatial autocorrelation refers to how a variable
  correlates with itself in space
• N number of samples
• i, j any two objects
• Xi value of attribute I
• Cij similarity of i and j attributes 1 if
  attribute data same
• Wij similarity of i and j locations
• Spatial auto correlation sum ( every cell in
  attribute x every cell in space)
• Use squared difference or products (Xi-Xj)2
• (Xi-mean X) (Xj-Mean X)

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Morans I

• One of the oldest indicators of spatial
  autocorrelation (Moran, 1950). Still a defacto
  standard for determining spatial autocorrelation
• Applied to zones or points with continuous
  variables associated with them.
• Compares the value of the variable at any one
  location with the value at all other locations

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Morans I

• Where N is the number of casesXi is the variable
  value at a particular locationXj is the variable
  value at another locationX is the mean of the
  variableWij is a weight applied to the
  comparison between location i and location j

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6. Measuring Distance Effects

• Sampling and interpolation is deductive
• Autocorrelation is inductive It measures
  strength of spatial auto-correlation in a map
• Moran Index is used to represent autocorrelation

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7. Establishing dependence in Scale

• Linear regression function Dependent and
  independent variables
• Linear the most simple but not always correct
• Generalization is the process of inference from
  the sample to larger group.
• Zero spatial autocorrelation made in many
  statistical inferences contradicts Toblers law
• Two phenomena over the same area can reveal
  similarities

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Fractals

• In selfsimilar objects each part has the same
  nature as the whole

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Induction and Deduction

• Induction Generalization from several examples
  to a common principle
• Deduction Specifying if a b and b c then ac.