Estimate Maximum Neighbors for kd-Tree Thinning — estimate_k

This function estimates the maximum value of k (the number of nearest neighbors) for kd-tree-based thinning by evaluating the densest regions of a spatial dataset. The function uses a histogram-based binning approach for efficiency and low memory usage.

Usage

estimate_k_max(coordinates, thin_dist, distance = c("haversine", "euclidean"))

Arguments

coordinates: A matrix of spatial coordinates with two columns for longitude and latitude.
thin_dist: A positive numeric value representing the thinning distance in kilometers. This defines the resolution of the grid used for density calculations.
distance: Distance metric used `c("haversine", "euclidean")`.

Value

A numeric value representing the maximum k (number of nearest neighbors) required for the densest regions in the dataset.

Details

The function divides the spatial domain into grid cells based on the specified thinning distance. Grid cell sizes are determined assuming approximately 111.32 km per degree (latitude/longitude). The function identifies the densest grid cells and their immediate neighbors to compute the maximum k value.

Examples

# Generate sample data
set.seed(123)
coordinates <- matrix(runif(200, min = -180, max = 180), ncol = 2)

# Estimate k for kd-tree thinning
k_max <- estimate_k_max(coordinates, thin_dist = 50)
print(k_max)
#> [1] 1