createAQuadtree {AQuadtree}

Create a Quadtree grid to anonymise spatial point data

Description

createAQuadtree returns a SpatialPointsDataFrame representing a Quadtree hierarchical geographic dataset. The resulting grid contains varying size cells depending on a given threshold and column. with identifiers A cellCode and cellNum is created for each cell as in INSPIRE Specification on Geographical Grid Systems.

Usage

createAQuadtree(
  points,
  dim = 1000,
  layers = 5,
  colnames = NULL,
  threshold = 100,
  thresholdField = NULL,
  funs = NULL,
  as = "Spatial",
  ineq.threshold = 0.25,
  loss.threshold = 0.4
)

Arguments

points

object of class "SpatialPoints" or "SpatialPointsDataFrame".

dim

a single integer specifying the initial cell sizes in meters, defaults to 1000.

layers

a single integer specifying the number of divisions of the initial cells, defaults to 5.

colnames

character or character vector specifying the columns to summarise in the resulting quadtree. For columns of class factor, a column for each factor level cill be created.

threshold

number. The threshold minimum value each cell must have in the column thresholdField.

thresholdField

character or character vector specifying the columns to which the threshold value will apply. If not specified, threshold value will be applied over the total cell points number. ThresholdField must be one of the colnames.

funs

character or character vector specifying the summary functions for each of the colnames. If vector, the size must be the same as colnames.

as

character indicating return type, if "AQuadtree" a quadtree class element will be returned, otherwise a SpatialPolygonsDataFrame will ber returned. Defaults to "Spatial".

ineq.threshold

inequality threshold value to be considered on the disaggregation process. Forces disaggregation under the given inequality threshold.

loss.threshold

loss threshold value to be considered on the disaggregation process. Stops disaggregation when there's much loss (i.e loss rate > ineq.threshold ).

Details

Given a set of points a varying size Quadtree grid is created performing a bottom-up aggregation considering a minimum threshold for each cell. Cells with a value under the threshold for the thresholdField are aggregated to the upper level in a quadtree manner.
When no thresholdField is given, total number of points in the cell will be used, and so, given a threshold of k, none of the cells in the resulting grid have a value less than k individuals as in a k-anonymity model.
The Quadtree produced balances information loss and accuracy. For instance, for the set of cells in the left image, where numbers in the cells represent the values in the thresholdField, using a threshold value of 100, the resulting Quadtree will be the one on the right. As we can see, some cells will be discarded, and some aggregated to maintain as much information as possible, keeping at the same time as much disaggregation as possible

The INSPIRE coding system for cell identifiers will be used to generate a cellCode and cellNum for each cell in the Quadtree. The objective of the coding system is to generate unique identifiers for each cell, for any of the resolutions.
The cellCode is a text string, composed of cell size and cell coordinates. Cell codes start with a cell size prefix. The cell size is denoted in meter (m) for cell sizes below 1000 m and kilometre (km) for cell sizes from 1000 m and above.
Examples: a 100 meter cell has an identifier starting with “100m”, the identifier of a 10000 meter cell starts with “10km”.
The coordinate part of the cell code reflects the distance of the lower left grid cell corner from the false origin of the CRS. In order to reduce the length of the string, Easting (E) and Northing (N) values are divided by 10^n (n is the number of zeros in the cell size value). Example for a cell size of 10000 meters: The number of zeros in the cell size value is 4. The resulting divider for Easting and Northing values is 10^4 = 10000.
The cellNum is a sequence of concatenated integers identifying all the hierarchical partitions of the main cell in which the point resides. For instance, the cellNum of the top right cell would be 416 (fourth in first partition, sixteenth in second partition)
The input object must be projected and units should be in 'meters' because the system uses the INSPIRE coding system.

Value

SpatialPolygonsDataFrame representing a varying size Quadtree aggregation for the given points.

See Also

• D2.8.I.2 INSPIRE Specification on Geographical Grid Systems – Guidelines https://inspire.ec.europa.eu/documents/Data_Specifications/INSPIRE_Specification_GGS_v3.0.1.pdf

• EEA reference grid dataset https://data.europa.eu/euodp/data/dataset/data_eea-reference-grids-2

Examples

data("CharlestonPop")
aQuadtree.Charleston<-createAQuadtree(CharlestonPop, threshold=10,
  colnames="sex", thresholdField=c("sex.male", "sex.female"))