Create a kernel function

Returns a closure K(xi, xj) suitable for use with all four psvr model fitting functions. The returned function accepts numeric vectors of any sign, which is required by the symmetric models (Models 2 and 4) that evaluate K(xk, -xl).

Usage

make_kernel(
  type = c("rbf", "linear", "polynomial"),
  sigma = 1,
  degree = 3L,
  coef0 = 1
)

Arguments

type

Kernel type: "rbf", "linear", or "polynomial".

sigma

Bandwidth for the RBF kernel, sigma > 0 (default 1).

degree

Integer degree for the polynomial kernel, degree >= 1 (default 3).

coef0

Constant term for the polynomial kernel (default 1).

Value

A function K(xi, xj) where xi and xj are numeric vectors of the same length, returning a scalar kernel evaluation.

Details

The three supported kernels are:

• RBF: K(xi, xj) = exp(-‖xi - xj‖² / (2 * sigma²))

• Linear: K(xi, xj) = xi · xj

• Polynomial: K(xi, xj) = (xi · xj + coef0)^degree

RBF and even-degree polynomial kernels satisfy Assumption 3 of the paper (kernel symmetry), making them compatible with the symmetric models. The linear kernel and odd-degree polynomial kernels do not satisfy Assumption 3 and should not be used with mape_sym_svr() or rmspe_sym_lssvr().

Examples

K <- make_kernel("rbf", sigma = 0.5)
K(c(1, 2), c(3, 4))
#> [1] 1.125352e-07

K_lin <- make_kernel("linear")
K_lin(c(1, 0), c(0, 1))
#> [1] 0

K_poly <- make_kernel("polynomial", degree = 2, coef0 = 1)
K_poly(c(1, 2), c(3, 4))
#> [1] 144