Geographic Theory and Geospatial Knowledge Discovery - Final

8/3/2019 Geographic Theory and Geospatial Knowledge Discovery - Final

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Geographic theory and geospatialknowledge discovery

Harvey J. MillerDepartment of Geography

University of Utah

[email protected] International Conference on Data Mining

Pisa, Italy 18 December 2008


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GIS trends

Geospatial technologies High-resolution monitors Location-aware technologies Geosensor networks etc, etc.

Atsunami of digital geo-data Increased volume

Giga to terabyte and beyond

Increased coverage Seamless databases

Increased spectrum Text, sound, imagery


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Introduction

Geospatial knowledgediscovery Human-centered process

of extracting novel,interesting and useful

patterns from geo-referenced data

A (very!) special case ofKDD

Location is important Observations are not independent Errors are often spatial Relationships are often local Non-linearity is typical Distributions are non-normal Highly multivariate but often

redundant Time often interacts with space Many data layers are categorical Data objects often cannot be

reduced to points Spatially aggregated data are

modifiable

Why is spatial special?- a mini course

- after Openshaw (1999)


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Introduction

Geographic theory and datamining There is a rich and

underexploited body ofgeographic theory

This can help guide the GKDprocess

Techniques

Background knowledge Pattern evaluation

etc Geography its notjust trivia!


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Great geographic theories

Spatial dependency Toblers first law Cartographic transformations

Spatial heterogeneity Spatial non-stationarity Disaggregate spatial statistics

Spatial interaction Spatial interaction theory Time geography

Spatial organization The concept of region Spatial logic


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What I will not talk about

The map One of the most

powerfultechnologies in the

history of civilization Still evolving!

Useful in GKD Interfaces

Pattern visualization

But, why the map?

Earliest known map ofthe world - sixth centuryB.C.E

www.antweb.orgGoogle Earth

www.gutenberg.org


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What I will not talk about

Domain theory Theories about processes specific to particular

domains Ecosystems biology, biogeography

Landscapes geology, geomorphology

Cities economics, political science, sociology,geography

These are theories with geospatial components,but are not uniquely geography


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What I am seeking and why

A theory of geography

- a unique perspective

-a coherent way ofthinking

- amenable to formal andcomputationalrepresentation

Framework fororganizing GKD

Suggest newtechniques and

strategies


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Spatial dependency

Toblers First Law ofGeography Everything is related to

everything else, but near thingsare related to more distant

things

Everything is related toeverything else

Spatial interdependency Near things are related to more

distant things Interdependency and proximity

Tobler, W. R. 1970. A computermovie simulating urban growthin the Detroit region. EconomicGeography46: 234-240.

Waldo Tobler receiving the 1999ESRI Lifetime Achievement

Award

Susanna Baumgart - UCSB


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Spatial dependency

Spatial autocorrelation Association based on geospatialproximity

Confounding

Something to be corrected e.g., econometrics

Informing Reveals information about

spatial process

e.g., spatial autocorrelationstatistics, spatial econometrics

esri.com

Body Mass Index in Salt Lake City, USA

Dr. Ikuho Yamada, University of Utah


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Spatial dependency

Spatial interpolation Estimate variables at

unobserved locationsusing values atobserved locations

Based on modeled

proximityrelationships

e.g., IDW, kriging

Spatial interpolation of influenzaover time in Europe 2004-2005www.eurosurveillance.org


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Spatial dependency

Geo-space

Proximity is the core oftheories of geo-space

Two main components Locations

Length metric

Formal theory Beguin and Thisse

(1979), others Admits a wide range of

length metrics Including semi-metrics

Miller and Wentz (2003)Annals, AAG

The fundamental tenet ofgeography:

Geo-space is explanatory


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Spatial dependency

Geo-space does not have to beEuclidean Geographic processes can follow

other metrics

Cartographic transformations Project geo-space based on:

Alternative proximity relationships

Smooth spatial heterogeneity

Why?

Visualization Improve explanation

CartoDraw Keim, North & Panse

Swedish migration map Hagerstrand (cited by Tobler 1963)


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Spatial dependency

Iceland in air passenger spaceAir passenger flows in Iceland

Cliff and Haggett (1998)

Spatial modeling of disease propagation in analternative geo-space


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Spatial dependency

Time-space maps Map with separation

measured in travel time

Why? Exploratory visualization Synoptic summary

Greater explanatory

power

Time-space transformationof Salt Lake City, USA

Nobbir Ahmed and Miller (2007)

Based on average daily traveltimes (vectors representdisplacements)


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Spatial dependency

Time-space transformations for 4 periods of the day morning, midday, afternoon and evening

1992 2001


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Spatial dependency

Solutions are sometimes > 3D

Highly stressed solution western SLC

Less stressful surfacerepresentation


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Spatial dependency

Comparing alternative spaces Bi-dimensional regression

Degree of fit between twoplanar configurations

After transformations,

rotations and translations Fit and significance

measures

Including spatial variation

Can be extended to higherdimensions

Nobbir Ahmed and Miller

Tobler (1994)


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Spatial heterogeneity

Geographic variationoccurs naturally Friction of distance

Relative location

Spatial processes arenon-stationary Apparent variation in

process with respectto location

If its stationary, itsnot spatial!

www.geovista.psu.edu


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Question: What do

Charles Darwin and PaulKrugman have incommon?

Besides beards

uk.gizmodo.com

ericblackink.minnpost.com


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Both recognized the power

of spatial heterogeneity Darwin

Observed geographic variationin species

Natural selection leads todifferences in species diversityand composition amongdifferent geographic locations

Long distance dispersal results

in geographic isolation andevolutionary divergence

uk.gizmodo.com


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Both recognized the power

of spatial heterogeneity Krugman

New economic geography

Geographic variation inproductive factors

Increasing returns enhancevariation and lead to greaterheterogeneity

ericblackink.minnpost.com


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Disaggregate spatialstatistics Decompose processes by

location Examples

Getis-Ord G K-function analysis Geographically weighted

regression

Unimaginable prior to

GIS! Data intensive Visually intensive

Local clustering of birth defects,

Shanxi province, China.

Wu et al (2004)www.biomedcentral.com


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Geographically weightedregression Assess spatial variation in

model structure Parameter estimates

Parameter errors

Goodness of fit

Influence

Determine whethervariation is systematic

Validate models betweendata subsets

Ask questions about spatialstructures in data

GWR with different spatial lags

Laffin, S. W. GeoComputation 99


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PARM_4

-1.857220 - -0.601224

-0.601223 - 0.055812

0.055813 - 0.787442

0.787443 - 1.664200

1.664201 - 3.123810

TVAL_4

-3.008610 - -2.580000

-2.579999 - -1.960000

-1.959999 - 1.960000

1.960001 - 2.580000

2.580001 - 5.342070

GWR: Spatial variation in the effect of social class onvoter turnout, Dublin Ireland

Parameter estimates t-tests

Fotheringham and Demsar (2009)


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GWR and visual insight Use visual analytics to

explore parameter space

Example SOM clusters based on

eight parameters

Cartographic visualization ofclusters



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GWR and visual insight Use visual analytics to

explore parameter space

Example Cluster selection

Parallel coordinate plot of

clusters across all eightvariables



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Spatial interaction

Spatial interaction theory Linkages and flows

between locations Spatial separation (-)

Complementarity (+)

Origin supply

Destination demand

Can be multidimensional

Map multiple variables intoa single measure

Originally an analogy with

Newtons Law ofGravitation, but


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Spatial interaction

spatial interaction has a

solid theoretical base Entropy maximization

Alan Wilson 1960s

Discrete choice theory Stewart Fotheringham

1980s which has resulted in awide spectrum of models Flow total constraints and

quasi-constraints Spatial association among

origins, destinations Behavioral processes etc, etc


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Spatial interaction

Data mining of spatialinteractions Existing techniques

Connections

Flows

Need better techniques Attributed flows

Spatial object dyads Origin-destination pairs

orgnet.com

CubeView detecting outliersin flows Shashi Shekhar

Visualizing social networks


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Spatial interaction

The death of distance? Distance is changing

High mobility Connectivity

Space-adjustingtechnologies (Ron Abler)

Change the nature ofspace with respect to thetime, cost and effort

Space-time convergence(Don Janelle)

Shrinking of distance dueto transport Rate per unit time

Janelle 1969

Convergence: Edinburgh andLondon 1658-1950


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Spatial interaction

Telepresence (Don Janelle) Participate in events without physical

presence

Space-time fragmentation (Helen Couclelis)

Spatial fragmentation Activities not tightly coupled with place

Temporal fragmentation Activities outside standard hours

Fluid time

Short planning horizons - Flocking

Need to expand theories of spatial interaction

Why let climbing a mountaininterfere with business?

Mt. Olympus, Utah, 18 June 2006


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Spatial interaction

Time geography Individual in geo-space

and time

Constraints imposed by:

Activity timing Activity locations Mobility resources

Ability to trade time forspace

Space-time path Realized movement

Paths in theory and practiceMeipo Kwan

Miller (2005)


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Spatial interaction

Time geography Individual in geo-space

and time

Constraints imposed by:

Activity timing Activity locations Mobility resources

Ability to trade time forspace

Space-time prism Potential movement

t

ija

ijt

jt

jxix

it

x

ijv

Prism in theory and practice

Miller andBridwell

(2009)


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Spatial interaction

Temporal Spatial

Presence Telepresence

Synchronous SP

Face-to-faceST

Telephone

TV

Asynchronous AP

Post-it notes

AT

Mail

EmailWebpages

Janelle (1995)

Communication modes basedon spatio-temporal constraints

Possible time geographic expressions

Relationsbetween

paths

Temporalevents


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Space-time cube: Visual analytic environment for

exploratory time geography Kraak and Huisman

Linking space-timepaths with attributes

Visualizing the intersection ofmultiple space-time prisms


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Spatial interaction

Interactive, multiscalevisualization of space-time paths Explore paths at

different levels ofspatio-temporalgranularity

Aggregation based onspatial similarity

and attributesimilarity (eventually) Tetsuo Kobayashi and Miller (in

progress)


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Spatial organization

The concept of region Partitioning of geographic space

based on homogeneity

Two types of region

Formal Explicit

Land cover, terrain, settlementpatterns

Functional

Implicit Organization, interactions,

linkages

www.desertmuseum.org

Formal regions basedon biogeography


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Regions and locationalprocesses Functional regions highlight the

interplay between spatialprocess and spatial pattern

Von Thunen bid-renttheory www.rri.wvu.edu

teacherweb.ftl.pinecrest.edu


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Central Place Theory Theory of the frequency,

size and spacing of citiesas market centers

wolf.readinglitho.co.uk

Nesting ofmarket

areas andcities

Distance Transport AdministrationWikipedia


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Spatial logic A route to explanation

Spatial logic: Pattern suggestsprocess

Process logic: Process suggestspatterns

Why? Patterns are integrated

manifestations of complexprocesses

Why not? Difficult to distinguish individualprocesses

Equifinality

Continental drift inferred

through spatial logic by AlfredWegener (1912)


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Geography and complexity Can spatial interaction explainintricate geographic patterns?

Complexity theory Simple, local interactions can

generate complex global behavior

Importance of geographic context Pattern and intensity ofinteractions


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The problem of arbitraryregions Arbitrary regions lead to

artifacts

Two types of effects Scale

Zoning

Solutions

Design optimal regions No regions!

Assess effects

10 15 5

5 10 15

5 10 5

n = 9; mean = 8.89

6.67 11.67 6.67

n= 3; mean = 8.34

7.5 11.25

6.67

n= 3; mean = 8.47

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7.5

n= 3; mean = 9.33

Modifiable Areal UnitProblem example(after Oliver; www.geog.ubc.ca)


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Is there a theory of geography?

Yes!

A unique perspectivefocusing on the role ofspatio-temporal proximity

Is it formal? Yes: geographers have

been building the formaland analytical foundationsof their field

Is it coherent? Yes, but it is not unified

Still need a grand unifiedtheory derived from firstprinciples

Corn van Elzakker ITC; www.itc.nl


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Opportunities and challenges

Spatial patterns & relations

Potentially large! Geo-theory can guide GKD

Background knowledge

Pattern evaluation

Background knowledge: challenges Geographic ontology

Concepts can be abstract, vague, multi-level

Knowledge extraction

Geo-theory: Implicit information Equations, algorithms, etc

KD: Explicit information Networks, hierarchies, rules

Concept hierarchy forlocation

- based on Han and Kamber

(2003)


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Spatial pattern evaluation

Reality = theory Interesting but not novel

Reality = null Not interesting or novel

Between theory and null Maybe interesting and novel

Problems What is a good spatial null?

Not Complete Spatial Randomness (CSR)

What is the metric? How do we measure spatial departures

from theory and null?


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Geographic theory as a pattern filter

Spatial data mining often generates alarge number of spatial and temporalpatterns and relationships

Meta-mining (Roddick 1999) Mining the results of previous mining

exercises

Derive higher-level patterns and

rules


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Algorithms and infrastructure Geographic models and

techniques can becomputationally complex

Often involve pairwise distances

between all geo-locations

Research needs

Heuristics

High-performance computing

This is a surprisingly under-researched area! 10 years old!


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Conclusion

Geographic theory Rich, coherent,

formal

Useful, butunderexploited indata mining

Waiting to bediscovered

wikimedia.org

Help fill the blank spots onthe map!


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Bibliography

Ahmed, N. and Miller, H. J. (2007) "Time-space transformations of geographic space for

exploring, analyzing and visualizing transportation systems," Journal of TransportGeography, 15, 2-17

Beguin, H., and J. F. Thisse. (1979) An axiomatic approach to geographical space,Geographical Analysis 11, 32541

Fotheringham, A. S. (1983) A new set of spatial-interaction models: The theory ofcompeting destinations, Environment and Planning A, 15, 1536.

Fotheringham, A. S. and Demar, U. (2009) Looking for a relationship? Try GWR? in H. J.Miller and J. Han (eds.) (2009) Geographic Data Mining and Knowledge Discovery - secondedition, Taylor and Francis, in press.

Getis, A., and J. K. Ord. (1992) The analysis of spatial association by use of distancestatistics, Geographical Analysis, 24, 189206.

Janelle, D. G. (1969) Spatial organization: A model and concept. Annals of the Association

of American Geographers 59: 34864. Links Janelle, D. G. (1995) Metropolitan expansion, telecommuting and transportation, in The

geography of urban transportation, ed. S. Hanson, 40734. New York: Guilford.


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Bibliography

Kraak, H. J. and Huisman, O. (2009) Beyond exploratory visualization of space-timepaths, in in H. J. Miller and J. Han (eds.) (2009) Geographic Data Mining and KnowledgeDiscovery - second edition, Taylor and Francis, in press.

Miller, H. J. (2004) "Tobler's First Law and spatial analysis" Annals of the Association ofAmerican Geographers, 94, 284-289.

Miller, H.J. (2005) "A measurement theory for time geography," Geographical Analysis, 37,17-45

Miller, H. J. (2005) "Necessary space-time conditions for human interaction," Environment

and Planning B: Planning and Design, 32, 381-401. Miller, H. J. and Bridwell, S. A. (2009), "A field-based theory for time geography," Annals of

the Association of American Geographers, 99 (in press).

Miller, H. J. and Wentz, E. A. (2003) "Representation and spatial analysis in geographicinformation systems," Annals of the Association of American Geographers, 93(3), 574-594.

Tobler, W. R. (1963) Geographic area and map projections. The Geographical Review 53:5978

Tobler, W. R. (1970) A computer movie simulating urban growth in the Detroit region,Economic Geography, 46, 234-240.

Tobler, W. R. (1994) Bi-dimensional regression, Geographical Analysis, 26, 187212

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Geographic Theory and Geospatial Knowledge Discovery - Final