Multivariate RBF Kernel

Source: R/kernels.R

Designed to be partially specified. (see examples)

SE(X, sigma = 1, rho = median(as.matrix(dist(t(X)))), jitter = 1e-10)

LINEAR(X, sigma = 1, c = rep(0, nrow(X)))

Arguments

X

covariate (dimension Q x N; i.e., covariates x samples)

sigma

scalar parameter

rho

scalar bandwidth parameter

jitter

small scalar to add to off-diagonal of gram matrix (for numerical underflow issues)

c

vector parameter defining intercept for linear kernel

Value

Gram Matrix (N x N) (e.g., the Kernel evaluated at each pair of points)

Details

Gram matrix G is given by

SE (squared exponential): $$G = \sigma^2 * exp(-[(X-c)'(X-c)]/(s*\rho^2))$$

LINEAR: $$G = \sigma^2*(X-c)'(X-c)$$