what’s special about spatial? -...
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What’s Special about Spatial?What’s Special about Spatial?
Michael F. GoodchildUniversity of California
Santa Barbara
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OutlineOutline
GISThe Center for Spatially Integrated Social Science (CSISS)The W matrix
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DefinitionsDefinitions
Spatial data– information about phenomena organized in
a spatial frame– the geographic frame
Spatial analysis– methods applied to spatial data that
• add value• reveal patterns and anomalies• support decisions
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The role of the GISThe role of the GIS
The infrastructure for handling data types– to spatial data as Excel is to tables, as S-
Plus is to statistical data, as Word is to text– spatial data or geographic data?– the housekeeper– the editor
The visualization tool
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The GIS data typesThe GIS data types
Discrete geographic features– points, lines, areas– the contents of maps– with associated attributes– countable– conceived as tables with associated
feature geometry
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FieldsFields
Geography as a collection of continuous variables– measured on nominal, ordinal, interval,
ratio scales– vector fields of direction and magnitude– exactly one value per point– z=f(x)– population density, land ownership, zoning
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Taxonomies of spatial analysisTaxonomies of spatial analysis
Thousands of methods– every one a command, menu item, icon, …
Based on data type– point pattern analysis– area (polygon) analysis– analysis of interactions– Bailey and Gatrell, Haining, Unwin
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A six-way conceptual classificationA six-way conceptual classification
Query and reasoningMeasurementTransformationDescriptive summaryOptimizationHypothesis testing
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Queries and reasoningQueries and reasoning
Real-time answers to geographic questions– Where is…?– What is this?– How do I get from here to here?
Based on alternative views of a database
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MeasurementsMeasurements
AreaDistanceLengthPerimeterSlope, aspectShape
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TransformationsTransformations
BufferingPoints in polygonsPolygon overlaySpatial interpolationDensity estimation
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City limits
Areas reachable in 5 minutes
Areas reachable in 10 minutes
Other areas
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Courtesy of Dick Block
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Descriptive summaryDescriptive summary
CentersMeasures of spatial dispersionSpatial dependenceFragmentationFractional dimension
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OptimizationOptimization
Design to achieve specific objectivesLocation of central point-like facilities to serve dispersed demandLocation of linear facilitiesDesign of boundaries for elections
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Hypothesis testingHypothesis testing
Geographic objects as a sample from a population– what is the population?
The independence assumption– the First Law of Geography– failure to find spatial dependence is always
a Type II error– hell is a place with no spatial dependence
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1564
2886
995
1990
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Information lost to the representationInformation lost to the representation
All sub-polygon spatial variationAll within-decade temporal variationAll identities– instead of <xy, person> we have
<R, number><xy, xy, xy, xy, …, R>
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2000
1970
1940
1910
A B C
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MaryJohn
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Challenges of GISChallenges of GIS
How to characterize what is missing?– error, accuracy, uncertainty
How to choose the best representation?– confounding influences
How to support many data models in a single software package
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Weaknesses of GISWeaknesses of GIS
There are too many possible data models– special-purpose GIS– lack of interoperability
Difficult to add data models retroactively
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Objectives, Structure, and History of CSISSObjectives, Structure, and History of CSISS
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Research infrastructureResearch infrastructure
Facilities that serve generic needs– economies of scale
The Hubble Telescope– high fixed costs distributed over many
usersInfrastructure funding at NSF– South Pole– advanced computation
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Generalizing the conceptGeneralizing the concept
Shared computational facilitiesShared data archiving and accessSoftware tools– shared licenses– shared development
Education and training– investments in skills– high leverage
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General principles:1. IntegrationGeneral principles:1. Integration
Linking data through common location– the layer cake
Linking processes across disciplines– spatially explicit processes– e.g. economic and social processes
interact at common locations
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2. Spatial analysis2. Spatial analysis
Social data collected in cross-section– longitudinal data are difficult to construct
Cross-sectional perspectives are rich in context– can never confirm process– though they can perhaps falsify– useful source of hypotheses, insights
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3. Spatially explicit theory3. Spatially explicit theory
Theory that is not invariant under relocationSpatial concepts (location, distance, adjacency) appear explicitlyCan spatial concepts ever explain, or are they always surrogates for something else?
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)(/)( ikkkijjiij dfAdfAEI Σ=
Eidij
Aj
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4. Place-based analysis4. Place-based analysis
Nomothetic - search for general principlesIdiographic - description of unique properties of placesAn old debate in Geography
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The Earth's surfaceThe Earth's surface
Uncontrolled varianceThere is no average placeResults depend explicitly on boundsPlaces as samplesConsider the model:y = a + bx
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5. Knowledge and policy5. Knowledge and policy
Policy requires the projection of general knowledge in spatial context– the implications of this process in this
location– alternative futures visualized under local
circumstancesGIS combines the general (processes, models, algorithms) with the specific (database of local details)
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6. Place-based search6. Place-based search
Location as an organizing dimension to information– much information can be georeferenced– much more than maps and images
The Geolibrary– what have you got about there?– impossible physically, feasible digitally
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Prototype geolibrariesPrototype geolibraries
National Geospatial Data Clearinghouse– www.fgdc.gov
Microsoft's Terraserver– terraserver.microsoft.com
Alexandria Digital Library– alexandria.ucsb.edu
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CSISS missionCSISS mission
The CSISS mission recognizes the growing significance of space, spatiality, location, and place in social science research. It seeks to develop unrestricted access to tools and perspectives that will advance the spatial analytic capabilities of researchers throughout the social sciences.
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Seven CSISS programsSeven CSISS programs
National WorkshopsSoftware ToolsVirtual CommunityBest Practice ExamplesPlace-Based SearchLearning ResourcesSpecialist Meetings
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The W MatrixThe W Matrix
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Abstraction of geographic spaceAbstraction of geographic space
Cartograms
Invariance under rotation, displacement, reflectionReconstruction from a distance matrixReconstruction from ranked distances– ordered metric data (Coombs)
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Space as a matrixSpace as a matrix
W where wij is some measure of interaction– adjacency– decreasing function of distance– invariant under rotation, displacement,
reflection– readily obtained from GIS– reflects a discrete object conceptualization
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The Modifiable Areal Unit ProblemThe Modifiable Areal Unit Problem
Openshaw and Taylor– 99 counties of Iowa– % Republican voters, % over 65
48 regions: -.548 to +.88612 regions: -.936 to +.996Solutions:– manipulate to determine range– strengthen theoretical framework
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Applications of the W matrixApplications of the W matrix
Spatial regression– add spatially lagged terms weighted by W– Anselin’s SPACESTAT
Moran and Geary indices of spatial dependence
( ) ( )( )∑∑ ∑
∑∑−
−−=
i j iiij
i jjiij
axw
xxwnc 2
2
2
1
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Social versus spatialSocial versus spatial
W estimatedWell-defined discrete object conceptualizationDirect measures of interaction
W calculatedDiscrete objects as arbitrary regions, MAUPSurrogate measures of interaction
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Cross-Product StatisticsCross-Product Statistics
Let C be a matrix of similarities between objectsConsider the cross-product
∑∑=Γi j
ijijwc
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Properties of ΓProperties of Γ
Generalizes Moran and GearyMeasures the correlation between social and spatialSimple randomization tests based on permutationHubert, Golledge, and Costanzo, Geographical Analysis 13(3): 224-233, 1981
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Social versus SpatialSocial versus Spatial
The ability to explain– empirical estimates versus measurements
Additional arguments supporting spatial– context– integration– implementation
A fruitful basis for collaboration