kerndwd (version 1.0.1)

kernel functions: Kernel Functions

Description

Kernel functions provided in the R package kernlab. Details can be seen in the reference below. "The Gaussian RBF kernel $k(x,x') = \exp(-\sigma \|x - x'\|^2)$ The Polynomial kernel $k(x,x') = (scale + offset)^{degree}$ The Linear kernel $k(x,x') = $ The Laplacian kernel $k(x,x') = \exp(-\sigma \|x - x'\|)$ The Bessel kernel $k(x,x') = (- Bessel_{(\nu+1)}^n \sigma \|x - x'\|^2)$ The ANOVA RBF kernel $k(x,x') = \sum_{1\leq i_1 \ldots < i_D \leq N} \prod_{d=1}^D k(x_{id}, {x'}_{id})$ where k(x,x) is a Gaussian RBF kernel. The Spline kernel $\prod_{d=1}^D 1 + x_i x_j + x_i x_j min(x_i, x_j) - \frac{x_i + x_j}{2} min(x_i,x_j)^2 + \frac{min(x_i,x_j)^3}{3}$."

Usage

rbfdot(sigma = 1)

polydot(degree = 1, scale = 1, offset = 1)

vanilladot()

laplacedot(sigma = 1)

besseldot(sigma = 1, order = 1, degree = 1)

anovadot(sigma = 1, degree = 1)

splinedot()

Arguments

sigma

The inverse kernel width used by the Gaussian, the Laplacian, the Bessel, and the ANOVA kernel

degree

The degree of the polynomial, bessel or ANOVA kernel function. This has to be an positive integer.

scale

The scaling parameter of the polynomial kernel function.

offset

The offset used in a polynomial kernel.

order

The order of the Bessel function to be used as a kernel.

Value

• Return an S4 object of class kernel which can be used as the argument of kern when fitting a kerndwd model.

Details

These R functions and descriptions are directly duplicated and/or adapted from the R package kernlab.

References

Wang, B. and Zou, H. (2015) ``Another Look at DWD: Thrifty Algorithm and Bayes Risk Consistency in RKHS". http://arxiv.org/abs/1508.05913v1.pdf Karatzoglou, A., Smola, A., Hornik, K., and Zeileis, A. (2004) ``kernlab -- An S4 Package for Kernel Methods in R", Journal of Statistical Software, 11(9), 1--20. http://www.jstatsoft.org/v11/i09/paper

Examples

# generate a linear kernel
kfun = vanilladot()

# generate a Laplacian kernel function with sigma = 1
kfun = laplacedot(sigma=1)

# generate a Gaussian kernel function with sigma = 1
kfun = rbfdot(sigma=1)

# set kern=kfun when fitting a kerndwd object
data(Haberman)
Haberman$X = scale(Haberman$X, center=TRUE, scale=TRUE)
lambda = 10^(seq(-3, 3, length.out=10))
m1 = kerndwd(Haberman$X, Haberman$y, kern=kfun, 
  qval=1, lambda=lambda, eps=1e-5, maxit=1e5)