Johnson-Lindenstrauss minimum dimension (Geron Ch 8, morie.fn grjll)

d >= 4 log(m) / (eps^2/2 - eps^3/3), ceiling-rounded.

Usage

morie_geron_johnson_lindenstrauss_bound(n_samples, eps)

Arguments

n_samples

At least 2.

eps

Distortion in (0, 1); may be a vector.

Value

List with min_dimension, exact, denominator, eps.

Examples

morie_geron_johnson_lindenstrauss_bound(n_samples = 5L, eps = 0.5)
#> $min_dimension
#> [1] 78
#> 
#> $exact
#> [1] 77.25302
#> 
#> $denominator
#> [1] 0.08333333
#> 
#> $eps
#> [1] 0.5
#> 
#> $n_samples
#> [1] 5
#> 
#> $estimate
#> [1] 78
#> 
#> $n
#> [1] 5
#>