Identify fixed-radius concentration hotspots — concentration

Identifies centre coordinates of fixed-radius circles with high local concentration. In insurance applications this can be used to find locations where the total insured value within a prescribed radius is largest.

Usage

concentration_hotspot(
  data,
  value,
  top_n = 1,
  radius = 200,
  cell_size = 100,
  grid_precision = 1,
  max_refinement_points = 1000,
  lon = "lon",
  lat = "lat",
  crs_metric = 3035,
  progress = TRUE,
  method = c("continuous", "grid", "observed")
)

Arguments

data: A data.frame containing point-level exposures. Must include columns for longitude, latitude, and the value of interest.
value: A string giving the name of the numeric column in data to aggregate within each radius.
top_n: Positive integer greater or equal to 1. Specifies how many non-overlapping hotspots are returned. Default is 1.
radius: Numeric. Radius of the circle in meters. This is typically the regulatory or scenario radius. Default is 200.
cell_size: Numeric. Size of the initial screening cells in meters. This is used by method = "continuous" and method = "grid". Smaller values give a finer initial search but increase computation time. method = "observed" searches observed point locations and does not use this value as a search-grid resolution. Default is 100.
grid_precision: Numeric. Approximate spacing in meters used for grid-based refinement. This is used by method = "grid" and by method = "continuous" only when the local subset is larger than max_refinement_points and the method falls back to grid refinement. It is not used by method = "observed". Smaller values evaluate more candidate centres and increase search precision. Default is 1.
max_refinement_points: Positive integer. Maximum number of local points used for pair-intersection refinement. If the local subset contains more points, method = "continuous" automatically falls back to the grid refinement used by method = "grid". Default is 1000.
lon: A string giving the longitude column in data. Default is "lon".
lat: A string giving the latitude column in data. Default is "lat".
crs_metric: Numeric. EPSG code for a projected CRS with meter units, used for distances, buffers, raster cells, and pair-intersection calculations. The default 3035 is ETRS89 / LAEA Europe and is a suitable default for Europe-wide applications. For other regions, choose a metric CRS appropriate to the study area, for example a local UTM zone, 5070 for the conterminous United States, or 3577 for Australia. For Asian portfolios there is no single universal choice; use a national projected CRS or the relevant UTM zone. Default is 3035.
progress: Logical. Whether to print progress messages for the main hotspot search steps. This is useful for larger portfolios and for top_n > 1. Default is TRUE.
method: Hotspot search strategy. "continuous" is the default and searches for a centre that may lie between observed points. "observed" searches only observed point locations as candidate centres. "grid" uses the original grid-refinement workflow.

Value

An object of class hotspot. The main components are hotspots, containing the selected centre coordinates and summed values, and contributing_points, containing the points inside the selected hotspot radii. The summed value column is named from value; for example, value = "amount" creates an amount_sum column. In contributing_points, data_row gives the row number of the contributing point in the original input data.

Details

The default method = "continuous" first uses terra rasterisation and focal sums to locate an approximate hotspot area. It then refines the local result by evaluating observed local points and the circle centres implied by local point pairs. The local refinement subset is chosen automatically around the terra-selected approximate centre, using a conservative margin based on radius and cell_size. If more than max_refinement_points local points are involved, it falls back to the grid refinement used by method = "grid". In that fallback case, grid_precision controls the local refinement grid; otherwise the pair-intersection step does not use grid_precision. The pair-refined result is exact only within the terra-selected local search area. The "observed" method is fast and deterministic, but can miss a larger hotspot when the optimal centre lies between observed points. The "grid" method uses a grid-based search with local refinement; smaller grid_precision values generally increase precision and computation time.

Author

Martin Haringa

Examples

portfolio <- Groningen[1:200, c("lon", "lat", "amount")]

hotspot <- concentration_hotspot(
  portfolio,
  value = "amount",
  radius = 200,
  cell_size = 100,
  progress = FALSE,
  top_n = 2
)

hotspot$hotspots
#>   id      lon      lat amount_sum
#> 1  1 6.554816 53.19424       1315
#> 2  2 6.572691 53.21873       1147
head(hotspot$contributing_points)
#> # A tibble: 6 × 7
#>      id data_row   lon   lat amount distance_m amount_sum
#>   <int>    <int> <dbl> <dbl>  <dbl>      <dbl>      <dbl>
#> 1     1       60  6.56  53.2    110       200.       1315
#> 2     1       66  6.56  53.2    728       112.       1315
#> 3     1      130  6.56  53.2     36       200.       1315
#> 4     1      159  6.56  53.2    441       192.       1315
#> 5     2        1  6.57  53.2     24       167.       1147
#> 6     2      134  6.57  53.2     23       165.       1147

observed_hotspot <- concentration_hotspot(
  portfolio,
  value = "amount",
  radius = 200,
  method = "observed",
  progress = FALSE
)

rbind(
  continuous = hotspot$hotspots[1, ],
  observed = observed_hotspot$hotspots
)
#>            id      lon      lat amount_sum
#> continuous  1 6.554816 53.19424       1315
#> observed    1 6.556074 53.19490       1205