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Geographical Information Systems and ScienceLongley P A, Goodchild M F, Maguire D J, Rhind D W (2001) John Wiley and Sons Ltd
5. The Nature of Geographic Data
© John Wiley & Sons Ltd
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Overview: Spatial is Special
The 'true' nature of geographic dataThe special tools needed to work with themHow we sample and interpolate (gaps)What is spatial autocorrelation, and how can it be measured?Fractals and geographic representation
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Why GIS?
Small things can be intricateGIS can:
Identify structure at all scalesShow how spatial and temporal context affects what we do
Allows generalization and accommodates errorAccommodates spatial heterogeneity
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Building Representations
Temporal and spatial autocorrelationUnderstanding scale and spatial structure
How to sample How to interpolate between observations
Object dimensionsNatural vs. artificial units
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Spatial Autocorrelation
Spatial autocorrelation is determined both by similarities in position, and by similarities in attributes
Sampling intervalSelf-similarity
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Spatial Sampling
Sample framesProbability of selectionAll geographic representations are samplesGeographic data are only as good as the sampling scheme used to create them
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Sample Designs
Types of samplesRandom samplesStratified samplesClustered samples
Weighting of observations
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Spatial Interpolation
Specifying the likely distance decaylinear: wij = -b dij
negative power: wij = dij-b
negative exponential: wij = e-bdij
Isotropic and regular – relevance to all geographic phenomena?
Inductive vs. deductive approaches
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Spatial Autocorrelation Measures
Spatial autocorrelation measures: Geary and Moran; nature of observations
Establishing dependence in space: regression analysis
Y = f (X1, X2 , X3 , . . . , XK)
Y = f (X1, X2 , X3 , . . . , XK) + ε
Yi = f (Xi1, Xi2 , Xi3 , . . . , XiK) + εi
Yi = b0 + b1 Xi1 + b2 Xi2 + b3 Xi3 + . . . bK XiK + εi
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Functional formThe assumptions of inference
Tobler’s LawMulticollinearity
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Discontinuous Variation
Fractal geometrySelf-similarityScale dependent measurementRegression analysis of scale relations
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Consolidation
Induction and deductionRepresentations build on our understanding of spatial and temporal structuresSpatial is special, and geographic data have a unique nature
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Fractals-Mandelbrot
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Serpinski’s Carpet
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Julia Set
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Fractals Cont’d
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How a Fractal Works (Koch Curve)
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Koch Curve-Infinite Length in a finite boundary
The initiator
The generator
The generator is repeated...
and repeated...
and repeated...
etc...