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kerntools (version 1.2.0)

Laplace: Laplacian kernel

Description

`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)

Value

Kernel matrix (dimension: NxN).

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)

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

Run this code
dat <- matrix(rnorm(250),ncol=50,nrow=5)
Laplace(dat,g=0.1)

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