How Far Is Too Far? - A Statistical Approach to Context-contingent Proximity Modeling

Proximity is a fundamental concept in any comprehensive ontology of space (Worboys 2001). The provision of a context-contingent translation mechanism between linguistic proximity measures (e.g. “near”, “far”) and metric distance measures is an important topic in current GIS research. After a discussion of context factors that mediate the relationship between linguistic and metric distance measures, we present a statistical approach, Ordered Logit Regression, to the context-contingent proximity modeling. The approach can predict proximity given the corresponding metric distance and context variables. An empirical case study with human subjects is carried out using this statistical approach. Interpretation and predictive accuracy of the empirical case study are discussed.

[1]  Eliseo Clementini,et al.  Qualitative Representation of Positional Information , 1997, Artif. Intell..

[2]  Mark Gahegan,et al.  Proximity Operators for Qualitative Spatial Reasoning , 1995, COSIT.

[3]  Eliseo Clementini,et al.  Qualitative Distances , 1995, COSIT.

[4]  A. Kaufman,et al.  Introduction to the Theory of Fuzzy Subsets. , 1977 .

[5]  Hans W. Guesgen,et al.  Reasoning About Distance Based on Fuzzy Sets , 2002, Applied Intelligence.

[6]  S. Stouffer.  Intervening opportunities: a theory relating mobility and distance , 1940 .

[7]  Hans W. Guesgen,et al.  Fuzzifying spatial relations , 2002 .

[8]  Gösta Ekman,et al.  Subjective geographic distance: A multidimensional comparison , 1973 .

[9]  Gordon D. Logan,et al.  A computational analysis of the apprehension of spatial relations , 1996 .

[10]  P. McCullagh.  Regression Models for Ordinal Data , 1980 .

[11]  D. Kemmerer.  “Near” and “far” in language and perception , 1999, Cognition.

[12]  Robert Allen Lowrey,et al.  Distance Concepts of Urban Residents , 1970 .

[13]  Edward K. Sadalla,et al.  An Information Storage Model for Distance Cognition , 1980 .

[14]  R. Wallace.  The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason , 1988 .

[15]  Jean-Claude Thill,et al.  Spatial queries with qualitative locations in spatial information systems , 2006, Comput. Environ. Urban Syst..

[16]  Daniel R. Montello,et al.  Spatial Information Theory A Theoretical Basis for GIS , 1995, Lecture Notes in Computer Science.

[17]  Ron Johnston,et al.  Spatial Behavior: A Geographic Perspective. Reginald G. Golledge and Robert J. Stimson; Seoul: The Making of a Metropolis. Joochul Kim and Sang-Chuel Choe , 1998 .

[18]  Daniel R. Montello,et al.  Scale and Multiple Psychologies of Space , 1993, COSIT.

[19]  A. Bonaert.  Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[20]  Peter Fisher,et al.  An investigation of the meaning of near and close on a university campus , 1991 .

[21]  A. Morris,et al.  A Framework for Modeling Uncertainty in Spatial Databases , 2003, Trans. GIS.

[22]  Jane Brennan,et al.  Foundations for a Formalism of Nearness , 2002, Australian Joint Conference on Artificial Intelligence.

[23]  G. Lakoff,et al.  Women, Fire, and Dangerous Things: What Categories Reveal about the Mind , 1988 .

[24]  John Freeman,et al.  The modelling of spatial relations , 1975 .

[25]  Jayant Sharma,et al.  A Qualitative Spatial Reasoner , 2000 .

[26]  T. Odlin,et al.  Fire and Dangerous Things: What Categories Reveal about the Mind , 1987 .

[27]  Richard W. Olshavsky,et al.  Perceptual maps of supermarket locations. , 1975 .

[28]  P. Thorndyke.  Distance estimation from cognitive maps , 1981, Cognitive Psychology.

[29]  V. B. Robinson.  Individual and multipersonal fuzzy spatial relations acquired using human-machine interaction , 2000, Fuzzy Sets Syst..

[30]  Daniel R. Montello,et al.  The Perception and Cognition of Environmental Distance: Direct Sources of Information , 1997, COSIT.

[31]  Andrew U. Frank,et al.  Qualitative spatial reasoning about distances and directions in geographic space , 1992, J. Vis. Lang. Comput..

[32]  Terence Lee.  Perceived Distance as a Function of Direction in the City , 1970 .

[33]  Edward K. Sadalla,et al.  The Perception of Traversed Distance , 1980 .

[34]  M. Kwan,et al.  Individual Accessibility Revisited: Implications for Geographical Analysis in the Twenty-first Century , 2003 .

[35]  Torsten Hägerstraand.  WHAT ABOUT PEOPLE IN REGIONAL SCIENCE , 1970 .

[36]  D. Sloane,et al.  An Introduction to Categorical Data Analysis , 1996 .

[37]  Vincent B. Robinson.  Interactive machine acquisition of a fuzzy spatial relation , 1990 .

[38]  Michael F. Worboys,et al.  Computational Structure in Three-Valued Nearness Relations , 2001, COSIT.

[39]  Michael F. Worboys,et al.  Nearness relations in environmental space , 2001, Int. J. Geogr. Inf. Sci..

[40]  Michael Worboys,et al.  Metrics and topologies for geographic space , 2001 .

[41]  Hans W. Guesgen,et al.  Imprecise reasoning in geographic information systems , 2000, Fuzzy Sets Syst..

[42]  Barbara Tversky,et al.  Spatial Information Theory A Theoretical Basis for GIS , 1993, Lecture Notes in Computer Science.

[43]  A. Agresti.  An introduction to categorical data analysis , 1997 .

[44]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[45]  Robert Lloyd,et al.  The Estimation of Distance and Direction from Cognitive Maps , 1989 .