rchemo (version 0.1-3)

krrda: KRR-DA models

Description

Discrimination (DA) based on kernel ridge regression (KRR).

Usage

krrda(X, y, weights = NULL, lb = 1e-5, kern = "krbf", ...)
# S3 method for Krrda
predict(object, X, ..., lb = NULL)

Value

For krrda:

fm

List with the outputs of the RR ((X): Training X-data (\(n, p\)); (K): Gram matrix; (Kt): Gram matrix; (U): intermediate output; (UtDY): intermediate output; (sv): singular values of the matrix (1,n); (lb): value of regularization parameter \(lambda\); (ymeans): the centering vector of Y (q,1); (weights): the weights vector of X-variables (p,1); (kern): kern function; (dots): Optional arguments.

lev

y levels

ni

number of observations by level of y

For predict.Krrda:

pred

matrix or list of matrices (if lb is a vector), with predicted class for each observation

posterior

matrix or list of matrices (if lb is a vector), calculated probability of belonging to a class for each observation

Arguments

X

For main function: Training X-data (\(n, p\)). --- For auxiliary function: New X-data (\(m, p\)) to consider.

y

Training class membership (\(n\)). Note: If y is a factor, it is replaced by a character vector.

weights

Weights (\(n\)) to apply to the training observations for the PLS2. Internally, weights are "normalized" to sum to 1. Default to NULL (weights are set to \(1 / n\)).

lb

A value of regularization parameter \(lambda\). If lb = 0, a pseudo-inverse is used in the RR.

kern

Name of the function defining the considered kernel for building the Gram matrix. See krbf for syntax, and other available kernel functions.

...

Optional arguments to pass in the kernel function defined in kern (e.g. gamma for krbf).

object

--- For auxiliary function: A fitted model, output of a call to the main functions.

Details

The training variable \(y\) (univariate class membership) is transformed to a dummy table containing \(nclas\) columns, where \(nclas\) is the number of classes present in \(y\). Each column is a dummy variable (0/1). Then, a kernel ridge regression (KRR) is run on the \(X-\)data and the dummy table, returning predictions of the dummy variables. For a given observation, the final prediction is the class corresponding to the dummy variable for which the prediction is the highest.

Examples

n <- 50 ; p <- 8
Xtrain <- matrix(rnorm(n * p), ncol = p)
ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE)

m <- 5
Xtest <- Xtrain[1:m, ] ; ytest <- ytrain[1:m]

lb <- 1
fm <- krrda(Xtrain, ytrain, lb = lb)
names(fm)
predict(fm, Xtest)

pred <- predict(fm, Xtest)$pred
err(pred, ytest)

predict(fm, Xtest, lb = 0:2)
predict(fm, Xtest, lb = 0)