Fig 1.
The density maps for the city of Fortaleza (Brazil) in logarithmic scale.
(a) The resident population (POP) by square kilometers (km2). (b) The floating population (FLO) by km2. (c) The disturbing the peace (DP) complaints by km2. (d) The property crimes (PC) by km2. The black circle highlights the downtown area of the city. This region has a low density of residents and disturbing the peace calls, and is dense in the flow of people and property crimes.
Fig 2.
Scattering plots by census tracts.
(a)-(d) All the plots between resident population (POP) and floating population (FLO) with police calls for disturbing the peace (DP) and for property crimes (PC) show uncorrelated behavior with the determination coefficients [44, 45] R2 < 0.15.
Fig 3.
The scheme of the City Clustering Algorithm (CCA).
Each polygon represents a clustering unit, specifically in our case, they represent census tracts. The light blue polygons are candidates for clustering (Di > D*); in contrast, the gray polygons cannot be clustered (Di ≤ D*). (a) The red dot represents the geometric center of the i–th census tract and the black circle with radius ℓ seeks neighbors belonging to the same cluster. (b)-(c) The same search operation is made for the other census tracts and is done until there are no more neighbors within the radius of operation. (d) The algorithm finishes running and the cluster is found.
Fig 4.
Behavior of exponent β by varying the parameters of the City Clustering Algorithm (CCA), ℓ and D*.
(a) The variation of β in correlation between the resident population (POP) and the disturbing the peace (DP) complaints is illustrated; (b) The variation is illustrated for correlations between the floating population (FLO) and the property crimes (PC). Both in (a) and (b), the x-axis represents ℓ, and this parameter was varied from 0 to 800 meters (m) (moment when the largest cluster consumes nearly the entire city); exponent β is shown on the y-axis. The colors of the lines represent the variation of the parameter D*, which corresponds to the resident population density in (a) and the floating population density in (b); this parameter was varied from 1000 to 8000. The shadows represent the standard error of coefficient β. It was not necessary to use values larger than 8000 because many census tracts start being discarded and the CCA can no longer form clusters. The graphs also show red dashed lines; between these lines is highlighted the range where, regardless of the parameterization, the exponent β has smaller ranges of variation. Finally, the dotted black line highlights exponent β = 1, in which the relationship between variables is isometric, in both graphs the exponent oscillates to low values of ℓ; in (a), the relationship is superlinear starting at ℓ ≥ 180 m; however in (b), superlinearity appears at ℓ ≥ 320 m (see S1 Appendix for the plots POP vs PC and FLO vs DP).
Fig 5.
Behavior of exponent α when varying the City Clustering Algorithm (CCA) parameters ℓ and D*.
(a) The variation of α in correlations between the resident population (POP) and the area (ARE) in square kilometers (km2) of clusters discovered with the CCA. (b) The variation for correlations between the floating population (FLO) and ARE. In (a) and (b), the x-axis represents the parameter ℓ, and the y-axis represents the exponent α. The line colors represent the variation of the parameter D*.
Fig 6.
The City Clustering Algorithm (CCA) applied to resident population (POP) and to floating population (FLO).
Each color represents a cluster; the light gray areas correspond to census tracts that were not grouped because they have Di < D*. (a) The population density was used in order to find the boundaries of the clusters with ℓ = 270 m and D* = 6000 resident people per km2. (b) The division found by considering urban mobility is shown; the map illustrated here was generated for ℓ = 320 m and D* = 2000 floating people per km2 in one day in Fortaleza.
Fig 7.
Scattering plots by City Clustering Algorithm (CCA).
The red lines represent the simple linear regressions applied to the data, the blue continuous lines represent the Nadaraya-Watson method [46, 47] and the blue dashed lines delimit the 95% confidence interval (CI) estimated by bootstrap. (a) A superlinear relationship was found, with exponent β = 1.15 ± 0.04, between the floating population (FLO) and the property crimes (PC). (b) A superlinear relationship was also found between the resident population (POP) and the disturbing the peace (DP) complaints, with exponent β = 1.18 ± 0.04. (c)-(d) The scattering plots of DP with FLO and PC with POP show an isometric relation was found between the variables, but with lower correlations than (a) and (b). The R2 is defined as determination coefficient [44, 45].