Neighbourhoods

Introduction

Representation allows us to determine whether a category is over-, under- or normally represented in the different areal units. We simply define neighbourhoods as the areal units where the different categories are overrepresented.

Measures

---

overrepresented_units (distribution, classes=None)

This functions outputs, for each category, a list of areal units where this category is overrepresented.

Parameters

• distribution dictionary

  Takes a dictionary of dictionaries with
  distribution[areal_unit][category] = number

• classes dictionary, optional

  Takes a dictionary of lists with classes[class] = [cat1, cat2, ...]
  If not specified, the algorithm will use the categories found in distribution

Output

• units dictionary

  Returns a dictionary of lists with
  units[category] = [unit1, ..., unitN]

---

neighbourhoods (distribution, areal_units, classes=None)

This function takes the distribution of income and the areal units' shape (as a Shapely Polygon object) and outputs the clusters where the different categories are overrepresented, or neighbourhoods.

Two areal units are said to belong to the same cluster if they are contiguous, i.e. if the intersection of their respective perimeter is a line.

Parameters

• distribution dictionary

  Takes a dictionary of dictionaries with
  distribution[unit_id][category] = number

• areal_units dictionary

  Takes a dictionary of Shapely Polygon objects with
  areal_units[unit_id] = areal_unit_polygon_object

• classes dictionary, optional

  Takes a dictionary of lists with classes[class] = [cat1, cat2, ...]
  If not specified, the algorithm will use the categories found in distribution

Output

• neighbourhoods dictionary

  Returns a dictionary of lists of lists with
  neighbourhoods[category] = [[unit in cluster1], ..., [units in cluster N]]

Examples

The following example shows how to extract the neighbourhoods using Marble, and plots a map of the city showing the units where category $1$ is overrepresented using matplotlib.

We assume that the distribution is contained in the variable city. The shape of the areal units are contained in a shapefile located at path/to/areal_units.shp.

import fiona
from shapely.geometry import shape

units = {}
with fiona.open('path/to/areal_units.shp', 'r', 'ESRI Shapefile') as source:
    for f in source:
       units[f['properties']['ID_FIELD']] = shape(f['geometry'])

This imports the areal units as Shapely Polygon Objects and stores them in the variable units.

import marble as mb

overrepresented = mb.overrepresented_units(city)

This finds the areal units where the different categories are overrepresented.

from maptlotlib import pylab as plt
from descartes import PolygonPatch

fig = plt.figure()
ax = fig.add_subplot(111)

for au in units:
    color = 'white'
    if au in overrepresented[1]:
        color = 'black' # Plot in black the units where 0 is overrepresented
    if units[au].geom_type=="Polygon":
        patch = PolygonPatch(units[au], fc=color, ec='None', alpha=1, zorder=1)
        ax.add_patch(patch)
    else:
        for t in units[au]:
            patch = PolygonPatch(t, fc=color, ec='None', alpha=1, zorder=1)
            ax.add_patch(patch)

ax.relim()
ax.axis('off')
ax.autoscale_view(True,True,True)
plt.show()

This plots the areal units where individuals belonging to category $1$ are overrepresented in black, and the others in white.