From Urban Segregation to Multifocal Pattern Detection

We develop a "multifocal" approach to reveal spatial dissimilarities in cities, from the most local scale to the metropolitan one. Think for instance of a statistical variable that may be measured at different scales, eg ethnic group proportions, social housing rate, income distribution, or public transportation network density. Then, to any point in the city there corresponds a sequence of values for the variable, as one zooms out around the starting point, all the way up to the whole city --~as if with a varifocal camera lens. The sequences thus produced encode in a precise manner spatial dissimilarities: how much they differ from perfectly random sequences is indeed a signature of the underlying spatial structure. We introduce here a mathematical framework that allows to analyze this signature and we provide a number of illustrative examples. Furthermore, this method may be used to detect and explore dissimilarities due to hidden spatial or non-spatial structures in statistical populations other than geo-social data, eg in ecological, biological or physical data.

[1]  S. Chakravorty.  A Measurement of Spatial Disparity: The Case of Income Inequality , 1996 .

[2]  B. Malmberg,et al.  Contextual effects on educational attainment in individualised, scalable neighbourhoods: Differences across gender and social class , 2015 .

[3]  Gilberto Câmara,et al.  Global and local spatial indices of urban segregation , 2007, Int. J. Geogr. Inf. Sci..

[4]  William A. V. Clark,et al.  A Multiscalar Analysis of Neighborhood Composition in Los Angeles, 2000–2010: A Location-Based Approach to Segregation and Diversity , 2015 .

[5]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[6]  Christopher Winship,et al.  The Welfare Approach to Measuring Inequality , 1980 .

[7]  William A. V. Clark,et al.  Measuring the Scale of Segregation Using k‐Nearest Neighbor Aggregates , 2015 .

[8]  Harvey Goldstein,et al.  Multilevel Modeling of Social Segregation , 2012 .

[9]  M. Barthelemy,et al.  Patterns of Residential Segregation , 2015, PloS one.

[10]  C. L. Mallows,et al.  Some Aspects of the Random Sequence , 1965 .

[11]  O. D. Duncan,et al.  A METHODOLOGICAL ANALYSIS OF SEGREGATION INDEXES , 1955 .

[12]  K. Taeuber,et al.  Population trends and residential segregation since 1960. Special censuses for 13 cities reveal increasing concentration of highly segregated Negroes. , 1968, Science.

[13]  Barbara J. Mills,et al.  Social Network Analysis in Archaeology , 2017 .

[14]  Thomas M. Stoker.  Completeness, Distribution Restrictions, and the Form of Aggregate Functions , 1984 .

[15]  Fabio Busetti,et al.  Quantile Aggregation of Density Forecasts , 2014 .

[16]  M. Fossett.  New Methods for Measuring and Analyzing Segregation , 2018 .

[17]  Christian Genest,et al.  Combining Probability Distributions: A Critique and an Annotated Bibliography , 1986 .

[18]  N. Saintier,et al.  Characterizing segregation in the Schelling-Voter model , 2017 .

[19]  R. Fisher,et al.  A New Test for 2 × 2 Tables , 1945, Nature.

[20]  L. Addario-Berry,et al.  Ballot Theorems, Old and New , 2008 .

[21]  Michael Batty,et al.  Cities and complexity - understanding cities with cellular automata, agent-based models, and fractals , 2007 .

[22]  N. Denton,et al.  The Dimensions of Residential Segregation , 1988 .

[23]  David Manley,et al.  Macro-, Meso- and Microscale Segregation: Modeling Changing Ethnic Residential Patterns in Auckland, New Zealand, 2001–2013 , 2015 .

[24]  Vasek Chvátal,et al.  The tail of the hypergeometric distribution , 1979, Discret. Math..

[25]  Donald O. Cowgill,et al.  An Index of Segregation Based on Block Statistics , 1951 .

[26]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[27]  M. Batty,et al.  Constructing cities, deconstructing scaling laws , 2013, Journal of The Royal Society Interface.

[28]  David R. James,et al.  Measures of segregation , 2019, Balancing School Choice and Equity.

[29]  R. Fisher.  Statistical methods for research workers , 1927, Protoplasma.

[30]  Flávia F. Feitosa,et al.  Countering Urban Segregation in Brazilian Cities: Policy-Oriented Explorations Using Agent-Based Simulation , 2012 .

[31]  Charles F. Cortese.  Further Consideration on the Methodological Analysis of Segregation Indices. , 1976 .

[32]  Clara Filet,et al.  An Attempt to Estimate the Impact of the Spread of Economic Flows on Latenian Urbanization1 , 2017, Front. Digit. Humanit..

[33]  M. White,et al.  The Measurement of Spatial Segregation , 1983, American Journal of Sociology.

[34]  J. M. Sakoda.  The checkerboard model of social interaction , 1971 .

[35]  Sean F. Reardon,et al.  2. Measures of Multigroup Segregation , 2002 .

[36]  Harvey Goldstein,et al.  A multilevel modelling approach to measuring changing patterns of ethnic composition and segregation among London secondary schools, 2001–2010 , 2015 .