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# Copyright (C) 2011 Julia Schiffner
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 or 3 of the License
# (at your option).
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# A copy of the GNU General Public License is available at
# http://www.r-project.org/Licenses/
#
#' Create a binary classification problem with V-shaped decision boundary.
#'
# details
#'
#' @title Create a Binary Classification Problem with V-shaped Decision Boundary
#'
#' @param n Number of observations.
#' @param d The dimensionality.
#' @param k Parameter to adjust the noise level.
#' @param data A \code{data.frame}.
#'
#' @return
#' \code{vData} returns an object of class \code{"locClass"}, a list with components:
#' \item{x}{(A matrix.) The explanatory variables.}
#' \item{y}{(A factor.) The class labels.}
#'
#' @examples
#' # Generate a training and a test set
#' train <- vData(1000)
#' test <- vData(1000)
#'
#' # Generate a grid of points
#' x.1 <- x.2 <- seq(0.01,1,0.01)
#' grid <- expand.grid(x.1 = x.1, x.2 = x.2)
#'
#' # Calculate the posterior probablities for all grid points
#' gridPosterior <- vPosterior(grid)
#'
#' # Draw contour lines of posterior probabilities and plot training observations
#' contour(x.1, x.2, matrix(gridPosterior[,1], length(x.1)), col = "gray")
#' points(train$x, col = train$y)
#'
#' # Calculate Bayes error
#' ybayes <- vBayesClass(test$x)
#' mean(ybayes != test$y)
#'
#' if (require(MASS)) {
#'
#' # Fit an LDA model and calculate misclassification rate on the test data set
#' tr <- lda(y ~ ., data = as.data.frame(train))
#' pred <- predict(tr, as.data.frame(test))
#' mean(pred$class != test$y)
#'
#' # Draw decision boundary
#' gridPred <- predict(tr, grid)
#' contour(x.1, x.2, matrix(gridPred$posterior[,1], length(x.1)), col = "red", levels = 0.5, add = TRUE)
#'
#' }
#'
#' @aliases vData vLabels vPosterior vBayesClass
#'
#' @rdname vData
#'
#' @export
#'
vData <- function (n, d = 2, k = 1) {
data <- matrix(runif(d * n), nrow = n)
posterior <- 0.5 + k * (data[,2] - 2 * abs(data[,1] - 0.5))
posterior[posterior < 0] <- 0
posterior[posterior > 1] <- 1
y <- as.factor(sapply(posterior, function(x) sample(1:2,
size = 1, prob = c(1 - x, x))))
data <- list(x = data, y = y)
class(data) <- c("locClass.vData", "locClass")
attr(data, "d") <- d
attr(data, "k") <- k
return(data)
}
#' @return \code{vLabels} returns a factor of class labels.
#'
#' @rdname vData
#'
#' @export
vLabels <- function(data, k = 1) {
d <- ncol(data)
posterior <- 0.5 + k * (data[,2] - 2 * abs(data[,1] - 0.5))
posterior[posterior < 0] <- 0
posterior[posterior > 1] <- 1
classes <- as.factor(sapply(posterior, function(x) sample(1:2, size = 1, prob = c(1-x,x))))
return(classes)
}
#' @return \code{vPosterior} returns a matrix of posterior probabilities.
#'
#' @rdname vData
#'
#' @export
vPosterior <- function(data, k = 1) {
d <- ncol(data)
posterior.2 <- 0.5 + k * (data[,2] - 2 * abs(data[,1] - 0.5))
posterior.2[posterior.2 < 0] <- 0
posterior.2[posterior.2 > 1] <- 1
posterior.1 <- 1 - posterior.2
posterior <- cbind(posterior.1, posterior.2)
colnames(posterior) <- paste("posterior", 1:d, sep = ".")
return(posterior)
}
#' @return \code{vBayesClass} returns a factor of Bayes predictions.
#'
#' @rdname vData
#'
#' @export
vBayesClass <- function(data, k = 1) {
d <- ncol(data)
posterior <- 0.5 + k * (data[,2] - 2 * abs(data[,1] - 0.5))
posterior[posterior < 0] <- 0
posterior[posterior > 1] <- 1
bayesclass <- as.factor(round(posterior) + 1)
return(bayesclass)
}
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