dkrr: Direct KRR Models

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

Direct KRR Models

Description

Direct kernel ridge regression (DKRR), following the same approcah as for DKPLSR (Bennett & Embrechts 2003). The method builds kernel Gram matrices and then runs a RR algorithm on them. This is not equivalent to the "true" KRR (= LS-SVM) algorithm.

Usage

dkrr(X, Y, weights = NULL, lb = 1e-2, kern = "krbf", ...)

## S3 method for class 'Dkrr'
coef(object, ..., lb = NULL)  

## S3 method for class 'Dkrr'
predict(object, X, ..., lb = NULL)  

Arguments

X	For the main function: Training X-data (n, p). — For the auxiliary functions: New X-data (m, p) to consider.
Y	Training Y-data (n, q).
weights	Weights (n, 1) to apply to the training observations. Internally, weights are "normalized" to sum to 1. Default to NULL (weights are set to 1 / n).
lb	A value of regularization parameter lambda.
kern	Name of the function defining the considered kernel for building the Gram matrix. See krbf for syntax, and other available kernel functions.
object	A fitted model, output of a call to the main function.
...	Optional arguments to pass in the kernel function defined in kern (e.g. gamma for krbf).

Value

See the examples.

References

Bennett, K.P., Embrechts, M.J., 2003. An optimization perspective on kernel partial least squares regression, in: Advances in Learning Theory: Methods, Models and Applications, NATO Science Series III: Computer & Systems Sciences. IOS Press Amsterdam, pp. 227-250.

Rosipal, R., Trejo, L.J., 2001. Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space. Journal of Machine Learning Research 2, 97-123.

Examples

n <- 6 ; p <- 4
Xtrain <- matrix(rnorm(n * p), ncol = p)
ytrain <- rnorm(n)
Ytrain <- cbind(y1 = ytrain, y2 = 100 * ytrain)
m <- 3
Xtest <- Xtrain[1:m, , drop = FALSE] 
Ytest <- Ytrain[1:m, , drop = FALSE] ; ytest <- Ytest[1:m, 1]

lb <- 2
fm <- dkrr(Xtrain, Ytrain, lb = lb, kern = "krbf", gamma = .8)
coef(fm)
coef(fm, lb = .6)
predict(fm, Xtest)
predict(fm, Xtest, lb = c(0.1, .8))

pred <- predict(fm, Xtest)$pred
msep(pred, Ytest)

lb <- 2
fm <- dkrr(Xtrain, Ytrain, lb = lb, kern = "kpol", degree = 2, coef0 = 10)
predict(fm, Xtest)

####### Example of fitting the function sinc(x)
####### described in Rosipal & Trejo 2001 p. 105-106 

x <- seq(-10, 10, by = .2)
x[x == 0] <- 1e-5
n <- length(x)
zy <- sin(abs(x)) / abs(x)
y <- zy + rnorm(n, 0, .2)
plot(x, y, type = "p")
lines(x, zy, lty = 2)
X <- matrix(x, ncol = 1)

fm <- dkrr(X, y, lb = .01, gamma = .5)
pred <- predict(fm, X)$pred
plot(X, y, type = "p")
lines(X, zy, lty = 2)
lines(X, pred, col = "red")

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