Full Toblerian Spaces: Recovering Tobler s Views on the Representations for Fluxes in Geographical Analysis

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1 Full Toblerian Spaces: Recovering Tobler s Views on the Representations for Fluxes in Geographical Analysis Marcio Azeredo - MsC Candidate (Applied Computer Science) Advisor: Dr. Antônio Miguel Vieira Monteiro INPE /2009

2 What is the importance of fluxes in Geographical Analysis? They can be used to represent spatial relationships in anisotropic space such as those involving demand for goods, services, or transfer of resources between geographic locations. Regional Space education service health service Security service Technology Money This property can be used to redesign the regional space according to the attributes involved in those spatial relationships represented.

3 How to analyze the dynamics of these fluxes? Using networks! Networks serves as ducts that lead fluxes, and its properties influence the preferred direction of connection between nodes. Different Network Properties Generate Different Fluxes Configurations Generate Different Spatial Configurations Using some of the Tobler s views! Bidimensional Regression is a method created to compare, two or more representations of the same configuration of points (Friedman and Kohler, 2003). The distortions observed represents the effort to transform one configuration to another.

4 Related Works Using Bidimensional Regression to redesign the space Salt Lake City Luxemburgo Ahmed and Miller(2007) Setúbal Peninsula Cauvin(2002) Dias et al. (2000)

5 Methodology Bidimensional Regression Valued Network Reference Space y Dissimilarity Matrix (edge value) n X u and v determination Resulting Space n T ij nxn (points) x n points Image Space Linear Transformation v Interpolation v v u u Multidimensional Analysis u and v determination u n points Distortion vectors start (x,y) end (u,v ) Entire space was interpolated n points Adapted from Cauvin(2005)

6 FTS Framework: Our Proposal Full Toblerian Spaces (FTS) is a proposed concept that embraces new forms of representation for anisotropics geographical spaces. This work is a small contribution. The framework FTS is designed to be a repository of classes written in C++, whose methods will work with the Terralib Open Plataform. User Web Desktop Web Processing Service (WPS) Plugin Bidimensional Regression Multidimensional Analysis Techniques Interpolation Techniques Others Techniques Terralib Library DBMSs Architecture

7 Current Stage (Testing FTS Framework) Time Attribute Railroad Network Number of Journeys Attribute

8 Perspectives The results of the proposed methodology can be used for.... making projections on the changes of the networks properties;.. identifying traffic congestions in transport networks;.. helping allocation of resources (ex. financial, human, material);.. assisting in the implementation of public policies. Case Study (two possibilities) Cities Influence Regions Research(IBGE,2008). Origin/Destination 2007 Research(Metrô, 2008) A set of Spreadsheets fluxes data.

9 Case Study Cities Influence Regions Research (IBGE,2008) Research by Brazilian Institute of Geography and Statistics. About search of goods and services (ex. universities, tv, internet, health, transportation). Origin/Destination 2007 Research (Metrô, 2008) Research by São Paulo Subway Company. About Urban Mobility and Metropolitan Spaces. São Paulo City (460 research areas).

10 References TOBLER, W. R. Bidimensional regression. Geographical Analysis, v. 26, n. 3, p , TOBLER, W. RTOBLER, W. R. (1987). Experiments in Migration Mapping by Computer. American Cartographer, TOBLER, TOBLER, W. R. Three Presentations on Geographical Analysis and Modeling. Technical Report 93-1, CAUVIN, C. A systemic approach to transport accessibility. a metodology developed in strasbourg: Cybergeo, n. 311, CAUVIN, C. Cognitive and cartographic representations: Towards a compreensive approach. Cybergeo, n. 206, DIAS, M. H.; CAUVIN, C.; ALEGRIA, M. F. Comparação de configurações cartográficas através da regressão bidimensional. Finisterra, v. 35, n. 69, p KRUSCAL J. B.; WISH, M. Multidimensional Scaling. Quantitative Aplications in The Social Sciences. Eric M. Uslaner

11 References IBGE. Regiões de Influência das Cidades. Rio de Janeiro - RJ: Instituto Brasileiro de Geografia e Estatística, METRÔ. Pesquisa OD Disponível em: < Acesso em: 15 agosto FRIEDMAN, A.; KOHLER, B. Bidimensional regression: Assessing the configural similarity and accuracy of cognitive maps and other two dimensional data sets. Psychological Methods, v. 8, n. 4, p , CÂMARA, G.; VINHAS, L.; QUEIROZ, G.; FERREIRA, K., MONTEIRO, A.M.V; CARVALHO, M. T.; CARTAXO, R.; CASANOVA, M. A.; FREITAS, U. M. TerraLib: An open-source GIS library for large-scale environmental and socio-economic applications. In: G. B. Hall, M. Leahy (eds.), Open Source Approaches to Spatial Data Handling. Berlin, Springer-Verlag, End