KernelICA (version 0.1.0)

kernel_matrix: Kernel Matrix Computation

Description

Computes kernel matrices for Gaussian and Hermite kernels.

Usage

kernel_matrix(
  x,
  y = x,
  kernel = c("gauss", "hermite"),
  sigma = 1,
  hermite_rank = 3
)

Arguments

x

Numeric vector.

y

Numeric vector, default is x.

kernel

Either "gauss" or "hermite".

sigma

Numeric value of the kernel variance. Default is 1.

hermite_rank

Rank of the Hermite kernel. Default is 3. Ignored, when the Gaussian kernel is chosen.

Value

A numeric kernel matrix.

Details

The function computes a matrix in the form of $(K_{ij}{)}_{(i,j)}=K(x_i,x_j)$ or $(K_{ij}{)}_{(i,j)}=K(x_i,y_j)$ for a kernel function $K$ depending if a second vector was given. The following two kernels are offered:

• Gaussian Kernel: $K(x,y)=e^{(x-y{)}^2/2{\sigma }^2}$

• Hermite Kernel: $K(x,y)=\sum _{k=0}^d{e}^{-x^2/2{\sigma }^2}{e}^{-y^2/2{\sigma }^2}\frac{h_k(x/\sigma )h_k(y/\sigma )}{2^{k}k!}$ where $h_k$ is the Hermite polynomial of grade $k$

Examples

# NOT RUN {
x <- rnorm(10)
kernel_matrix(x, kernel = "gauss", sigma = 4)
kernel_matrix(x, kernel = "hermite", sigma = 4, hermite_rank = 3)
# }