rbfkernel {rdetools} | R Documentation |
Calculates the RBF kernel matrix for the dataset contained in the matrix X
,
where each row of X
is a data point. If Y
is also a matrix (with the
same number of columns as X
), the kernel function is evaluated between all
data points of X
and Y
.
rbfkernel(X, sigma = 1, Y = NULL)
X |
matrix containing a data point in each row |
sigma |
kernel width of rbf kernel |
Y |
leave this NULL if the kernel function should be evaluated between the data points only contained in
X (which can be regarded as Y = X ) or to a matrix with same number of columns as X
if you want to evaluate the function between the points of X and Y |
Each row of X
must be a data point, i.e. X = (x_1, x_2, ..., x_n).
The kernel matrix K
is then defined as
K = (k(x_i, x_j)), i,j=1,...,n
If Y
is not NULL and also contains data points in each row, i.e. Y = (y_1, y_2, ..., y_m),
the kernel matrix K
of X
and Y
is defined as
K = (k(x_i, x_j)), i=1,...,n, j=1,...,m
In this case, k is the rbf (radial basis function) kernel, which is defined as
k(x, y) = exp(-0.5*||x - y||^2/sigma)
where x, y are data points and sigma is the rbf kernel width.
RBF kernel matrix K
for the given dataset
Jan Saputra Mueller
## generate sinc data and calculate rbf kernel matrix with sigma = 1 d <- sincdata(100, noise = 0.1) K <- rbfkernel(d$X)