kernel_matrix: Kernel Matrix Computation

In KernelICA: Kernel Independent Component Analysis

Kernel Matrix Computation

Description

Computes kernel matrices for Gaussian and Hermitian 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.

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:

• Gauss 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

Value

A numeric kernel matrix.

Examples

x <- rnorm(10)
kernel_matrix(x, kernel = "gauss", sigma = 4)
kernel_matrix(x, kernel = "hermite", sigma = 4, hermite_rank = 3)

KernelICA documentation built on Aug. 4, 2026, 9:07 a.m.