Laplacian kernel — Laplace • kerntools

`Laplace()` computes the laplacian kernel between all possible pairs of rows of a matrix or data.frame with dimension NxD.

Usage

Laplace(X, g = NULL)

Arguments

X: Matrix or data.frame that contains real numbers ("integer", "float" or "double").
g: Gamma hyperparameter. If g=0 or NULL, `Laplace()` returns the Manhattan distance (L1 norm between two vectors). (Defaults=NULL)

Value

Kernel matrix (dimension: NxN).

Details

Let $x_i,x_j$ be two real vectors. Then, the laplacian kernel is defined as: $$K_{Lapl}(x_i,x_j)=\exp(-\gamma \|x_i - x_j \|_1)$$

Examples

dat <- matrix(rnorm(250),ncol=50,nrow=5)
Laplace(dat,g=0.1)
#>             1           2           3            4            5
#> 1 1.000000000 0.002934677 0.013209824 0.0055161209 0.0038626609
#> 2 0.002934677 1.000000000 0.004009897 0.0024804715 0.0026005123
#> 3 0.013209824 0.004009897 1.000000000 0.0042107338 0.0031150382
#> 4 0.005516121 0.002480471 0.004210734 1.0000000000 0.0009941164
#> 5 0.003862661 0.002600512 0.003115038 0.0009941164 1.0000000000