Curse of dimensionality (Geron Ch 8, morie.fn hmcod)

Exact uniform-cube nearest-neighbour radius r = exp((lgamma(d/2 + 1) - log n - (d/2) log pi) / d), the mean pairwise distance sqrt(d/6), and the border share.

Usage

morie_geron_curse_dimensionality(d, n)

Arguments

d

Dimensions.

n

Sample size.

Value

List with nn_distance, mean_pairwise_distance, border_fraction, border_tolerance, n_for_density, sparsity_factor, d, estimate, n.

Examples

morie_geron_curse_dimensionality(d = 5L, n = 5L)
#> $nn_distance
#> [1] 0.5199317
#> 
#> $mean_pairwise_distance
#> [1] 0.9128709
#> 
#> $border_fraction
#> [1] 0.00996008
#> 
#> $border_tolerance
#> [1] 0.001
#> 
#> $n_for_density
#> [1] 18997.72
#> 
#> $sparsity_factor
#> [1] 5.199317
#> 
#> $d
#> [1] 5
#> 
#> $estimate
#> [1] 0.5199317
#> 
#> $n
#> [1] 5
#> 
#> $method
#> [1] "exact uniform-cube nearest-neighbour radius, mean pairwise distance and border share"
#>