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.
gausskernel(X = NULL, sigma = NULL)
N by N numeric data matrix.
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_i1-x_j1)^2 + (x_i2-x_j2)^2 + ... + (x_iD-x_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.
X <- matrix(rnorm(6),ncol=2) gausskernel(X=X,sigma=1)
## KRLS Package for Kernel-based 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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