Julie Sungsoon Hwang & Jean-Claude ThillDepartment of GeographyState University of New York at BuffaloU.S.A.
August 24, 200411th Int’l Symposium of Spatial Data Handling
Empirical study on location indeterminacy of localities
Research question
How can we represent vague concepts of spatial object in a (discrete) computing environment (e.g. GIS)?
Nearness in localities
Mental maps of localities
Indeterminate boundaries of localities
Research scope
Mental maps Generals: f (distance, relation, scale) Specifics : f (preferences, experience, …)
Localities Official recognition: eg. administrative unit Unofficial recognition: eg. vernacular region
Research objective [1]
Building the model of locality boundary using fuzzy regions (egg-yolk model) and some rules regarding nearness
0
1
BA
A
B
2-Dimensional Geographic Space
x: 1-Dimensional Geographic SpaceY: Degree of Membership
Research objective [2]
Examining any difference in location indeterminacy between urban and rural settings
BuffaloBuffalo
Urban
WilsonWilson
Rural
Example: identifying localities…
Accident location?
Which city?
Task 1: theoretical
Building the model of locality boundary using fuzzy region and rules of nearness
Fuzzy regions
Core
Exterior
Boundary
Nearness
= Fuzzy set membership of belonging to “Syracuse”
Near “Syracuse”?
What determines the fuzzy set membership What determines the fuzzy set membership function value?function value?
Euclidean distanceEuclidean distance Spatial qualitative relationSpatial qualitative relation Scale-dependentScale-dependent
Locality as a fuzzy region
Exterior
Core
Boundary1stOrderGr2ndOrderGr
Computing fuzzy set membership value in GIS: work steps
1. Delineate boundaries
2. Assign membership values
3. Create TINs 4. Interpolate values on TINs
Computing fuzzy set membership value in GIS: results
ELMA
AMHERST
BUFFALO
CLARENCE
ALDEN
NEWSTEAD
WALESHAMBURG AURORA
LANCASTER
MARILLA
ROYALTON
ORCHARD PARK
PENDLETON
GRAND ISLAND
DARIEN
WHEATFIELD
BENNINGTON
CHEEKTOWAGA
SHELDON
ALABAMA
TONAWANDA
WEST SENECA
LOCKPORT
PEMBROKE
NIAGARA FALLS
NIAGARA
EVANS
NORTH TONAWANDA
LACKAWANNA
SHELBY
EDEN
Legend
County Boundary
TownorCity Boundary (PLACE_PL)
WaterBody
FuzzySet Membership of Locality
Value
High : 1
Low : 0
¯
0 7,500 15,0003,750 Meters
Lake Erie
Comparison to other proximity measures
core exterior0.5-cut boundary
0.5-cut boundary
0.5
1
0.5
1
coreexterior0.5-cut boundary
core
Distance Buffer Fuzzy proximity
Task 2: empirical
Examining any difference in location indeterminacy between urban and rural settings
Georeferencing traffic accident data
We considered 5460 out of 8631 cases from NYS ‘96-’01Of these, 246 urban, and 298 rural localities are compared
Computing location indeterminacy index of localities
i = 1 - (Σi)/n
78% sure
95% sure
58% sure
Comparing location indeterminacy index of urban versus rural localities
Average number of fatal crashes in rural areas is 2 whereas those in urban areas is 16
To work around small number problem, we compute Bayesian estimates of both groups adjusted for within-group distributions
People are 94% (or somewhere between 93% and 95%) sure in identifying urban localities while they are 88% (or somewhere between 86% and 90%) sure in identifying rural localities
ANOVA
Analysis of variance conducted on Bayesian estimates of location indeterminacy confirms the difference between urban versus rural locality is significant in terms of location indeterminacy
Neighborhood types may affect the degree of certainty to which the boundary of locality is perceived
Interpretation of results
• Mental maps of urban settings may be less error-prone than those of rural settings
• Spatial knowledge acquisition: city provides more landmark or route upon which judgment on indeterminate boundaries of localities can be based
• Scale factor: dense urban settings provide a reasonable scale in which humans can conceptualize localities without much difficulty
Conclusions
Fuzzy set theory provides a reasonable mechanics to represent vague concept of geospatial objects
Neighborhood types affect the way humans acquire spatial knowledge and forge mental representations of it