Find highest concentration — find_highest_concentration • spatialrisk

Identifies the central coordinates of a circle with a fixed radius that maximizes the coverage of demand points.

Usage

find_highest_concentration(
  df,
  value,
  top_n = 1,
  radius = 200,
  cell_size = 100,
  grid_precision = 1,
  lon = "lon",
  lat = "lat",
  crs_metric = 3035,
  print_progress = TRUE
)

Arguments

df: A data.frame containing demand points. Must include at least columns for longitude, latitude, and the value of interest.
value: Column name in df with the value of interest to summarize.
top_n: Positive integer greater or equal to 1 (default is 1). Specifies how many highest concentration circles are returned. If top_n > 1, then after each iteration the points belonging to the highest concentration are removed from df. This prevents the subsequent concentrations from being located in the same area, which would otherwise repeatedly select overlapping points with the largest values.
radius: Numeric. Radius of the circle in meters (default = 200).
cell_size: Numeric. Size of the grid cell in meters (default is 100). Defines the resolution of the initial raster grid. The choice of cell size depends on the size of the study area. For example, for a country the size of the Netherlands, cells of 100 × 100 meters are typically sufficient. For larger areas such as Germany, a cell size of 200 × 200 meters may be more appropriate. The choice of cell_size does not affect the final result, only the computational speed.
grid_precision: Numeric. Precision of the search grid in meters (default is 1). Determines the spacing of sub-points within each raster cell. For example, with cell_size = 100 and grid_precision = 1, 10,000 sub-points (100 × 100) are evaluated per cell. Larger values reduce the number of sub-points (and runtime), but also reduce spatial accuracy.
lon: Column name in df for longitude (default = "lon"). Must be in EPSG:4326.
lat: Column name in df for latitude (default = "lat"). Must be in EPSG:4326.
crs_metric: Numeric. Metric Coordinate Reference System (CRS) used in background calculations. For Europe use EPSG:3035 (default). For the United States use EPSG:6317. For Asia-Pacific use EPSG:8859.
print_progress: Logical. Whether to print progress messages (TRUE/FALSE).

Value

A list with two elements:

A data.frame with the top_n highest concentrations.
A data.frame with the subset of df corresponding to those concentrations.

Details

A recent regulation by the European Commission mandates insurers to report the maximum insured value of fire risk policies for all buildings partly or fully within a circle of radius 200 meters (see Article 132 - fire risk sub-module - of the Delegated Regulation). This captures the risk of catastrophic fire or explosion, including terrorist attacks.

The problem resembles a Maximal Covering Location Problem (MCLP) with a fixed radius, a classic facility location problem. The goal is to select the best locations to maximize coverage of demand points, ensuring each demand point lies within the radius of at least one selected facility.

References

Commission Delegated Regulation (EU) (2015). Solvency II Delegated Act 2015/35. Official Journal of the European Union, 58:124.

Author

Martin Haringa

Examples

# Find single highest concentration
x <- find_highest_concentration(Groningen, value = "amount")
plot(x)

# Find top 2 concentrations with smaller grid cells
y <- find_highest_concentration(Groningen, "amount",
                                top_n = 2, cell_size = 50)
#> 
Finished 1 of 2
Finished 2 of 2
plot(y)