Description Usage Arguments Details Value Author(s) See Also Examples
Given a N by D numeric data matrix, this function computes the N by N distance matrix with the pairwise distances between the rows of the data matrix as measured by a Gaussian Kernel.
1  gausskernel(X = NULL, sigma = NULL)

X 
N by N numeric data matrix. 
sigma 
Positive scalar that specifies the bandwidth of the Gaussian kernel (see details). 
Given two D 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 given by
x_i  x_j=((x_i1x_j1)^2 + (x_i2x_j2)^2 + ... + (x_iDx_jD)^2)^.5
and sigma^2 is the bandwidth of the kernel.
Note that the Gaussian kernel is a measure of similarity between x_i and x_j. It evalues to 1 if the x_i and x_j are identical, and approaches 0 as x_i and x_j move further apart.
The function relies on the dist
function in the stats package for an initial estimate of the euclidean distance.
An N by N numeric distance matrix that contains the pairwise distances between the rows in X.
Jens Hainmueller (Stanford) and Chad Hazlett (MIT)
dist
function in the stats package.
1 2  X < matrix(rnorm(6),ncol=2)
gausskernel(X=X,sigma=1)

## KRLS Package for Kernelbased Regularized Least Squares.
## See Hainmueller and Hazlett (2014) for details.
1 2 3
1 1.0000000 0.1034381 0.1863869
2 0.1034381 1.0000000 0.5184201
3 0.1863869 0.5184201 1.0000000
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