R/RBF_K.R

In Luisiglm/KBoost: Inference of gene regulatory networks from gene expression data

#' Function to calculate the RBF Kernel of a matrix X with width g.
#'
#' @param x an Nx1 numeric matrix with N observations.
#' @param g a positive scalar with the width parameter.
#' @export
#' @return the matrix with the RBF kernel
#' @examples
#' x = rnorm(100,0,1)
#' k = RBF_K(x,40)
#'
RBF_K <- function(x,g){
    # formula K(i,j) = exp(-Euc[i,j]/g), Euc is the Squared Euclidean distance.
    # Calculate the Squared Euclidian Distance between Every Observation.
    # Euc[i,j] = (x[i]-x[j])^2 = x[i]^2 - 2x[i]*x[j]-x[j]^2.
    # In matrix operations it yields the following:
    x2 <- x^2
    X <- matrix(x,length(x),length(x))
    X2 <- matrix(x2, length(x),length(x))
    # Take the exponential and divide it by g.
    K <- exp(-(X2-2*X*t(X)+t(X2))/g)
    return(K)
}