gram: Kernel functions

In mlesnoff/rchemo: Dimension reduction, Regression and Discrimination for Chemometrics

Kernel functions

Description

Building Gram matrices for different kernels (e.g. Scholkopf & Smola 2002).

- radial basis: exp(-gamma * |x - y|^2)

- polynomial: (gamma * x' * y + coef0)^degree

- sigmoid: tanh(gamma * x' * y + coef0)

Usage

krbf(X, Y = NULL, gamma = 1)

kpol(X, Y = NULL, degree = 1, gamma = 1, coef0 = 0)

ktanh(X, Y = NULL, gamma = 1, coef0 = 0)

Arguments

X	Dataset (n, p).
Y	Dataset (m, p). The resulting Gram matrix K(X, Y) has dimensionnality (n, m). If NULL (default), Y is set equal to X.
gamma	See the code.
degree	See the code.
coef0	See the code.

Value

See the examples.

References

Scholkopf, B., Smola, A.J., 2002. Learning with kernels: support vector machines, regularization, optimization, and beyond, Adaptive computation and machine learning. MIT Press, Cambridge, Mass.

Examples

n <- 5 ; p <- 3
Xtrain <- matrix(rnorm(n * p), ncol = p)
Xtest <- Xtrain[1:2, , drop = FALSE] 

gamma <- .8
krbf(Xtrain, gamma = gamma)

krbf(Xtest, Xtrain, gamma = gamma)
exp(-.5 * euclsq(Xtest, Xtrain) / gamma^2)

kpol(Xtrain, degree = 2, gamma = .5, coef0 = 1)

mlesnoff/rchemo documentation built on April 15, 2023, 1:25 p.m.