R/kmatrixGauss.R

In terrytangyuan/lfda: Local Fisher Discriminant Analysis

#' Gaussian Kernel Computation
#' (Particularly used in Kernel Local Fisher Discriminant Analysis)
#'
#' Gaussian kernel computation for klfda, which maps the original
#' data space to non-linear and higher dimensions.
#'
#' @param x n x d matrix of original samples.
#'          n is the number of samples.
#' @param sigma dimensionality of reduced space. (default: 1)
#'
#' @return K n x n kernel matrix.
#'           n is the number of samples.
#'
#' @keywords klfda kernel local fisher discriminant
#'           transformation mahalanobis metric
#'
#' @aliases kmatrixGauss
#'
#' @author Yuan Tang
#'
#' @seealso See \code{klfda} for the computation of
#'          kernel local fisher discriminant analysis
#'
#' @export kmatrixGauss
#'
#' @references
#' Sugiyama, M (2007).
#' Dimensionality reduction of multimodal labeled data by
#' local Fisher discriminant analysis.
#' \emph{Journal of Machine Learning Research}, vol.\bold{8}, 1027--1061.
#'
#' Sugiyama, M (2006).
#' Local Fisher discriminant analysis for supervised dimensionality reduction.
#' In W. W. Cohen and A. Moore (Eds.), \emph{Proceedings of 23rd International
#' Conference on Machine Learning (ICML2006)}, 905--912.
#'
#' https://shapeofdata.wordpress.com/2013/07/23/gaussian-kernels/
#'
#' @examples
#'
#' kmatrixGauss(iris[, -5])
kmatrixGauss <- function(x, sigma = 1) {
  x <- t(as.matrix(x))
  d <- nrow(x)
  n <- ncol(x)
  X2 <- t(as.matrix(colSums(x^2)))
  distance2 <- repmat(X2, n, 1) + repmat(t(X2), 1, n) - 2 * t(x) %*% x
  K <- exp(-distance2 / (2 * sigma^2))
  return(K)
}