This function computes and returns a distance matrix
computed by using a Gaussian Kernel distance measure to compute the distances between the rows of a data matrix.
Usage
gausskernel(X = NULL, sigma = NULL)
Arguments
X
an n by k numeric matrix.
sigma
a scalar value that specifies the width of the Gaussian kernel sigma^2 (see details).
Value
An n by n numeric distance matrix that contains the pairwise distances between teh rows of X.
Details
Given two k dimensional vectors x_i and x_j. The Gaussian kernel is defined as: k(x_i,x_j)= exp(-|| x_i - x_j ||^2/sigma^2).
Where ||x_i - x_j|| is the Euclidean distance between x_i and x_j ||x_i - x_j||=((x_i1-x_j1)^2 + (x_i2-x_j2)^2 + ... + (x_ik-x_jk)^2)^.5.
Note that the Gaussian kernel is a measure of similarity between the two input vectors
(it evalues to 1 if the two input arguments are identical, and approaches 0 as the two vectors get very far apart.).
The function relies on the dist function in the stats package for an initial estimate of the euclidean distance.