#' Function to generate a unit space for the Mahalanobis-Taguchi (MT) method
#'
#' \code{MT} generates a unit space for the Mahalanobis-Taguchi (MT) method. In
#' \code{\link{general_MT}}, the inversed correlation matrix is used for A and
#' the data are normalized based on \code{unit_space_data}.
#'
#' @param unit_space_data Matrix with n rows (samples) and p columns (variables).
#' Data to generate the unit space. All data should be
#' continuous values and should not have missing values.
#' @param includes_transformed_data If \code{TRUE}, then the transformed data
#' are included in a return object.
#' @param ... Passed to \code{\link[base]{solve}} for computing the inverse of
#' the correlation matrix.
#'
#' @return \code{MT} returns an object of S3 \link[base]{class} "MT". An object
#' of class "MT" is a list containing the following components:
#'
#' \item{A}{p x p (q x q) matrix. Inversed correlation matrix of
#' \code{unit_space_data} (the transformed data).}
#' \item{calc_A}{\code{function(x) solve(cor(x), ...)}.}
#' \item{transforms_data}{Function to be generated from
#' \code{\link{generates_normalization_function}} based
#' on \code{unit_space_data}.}
#' \item{distance}{Vector with length n. Distances from the unit space to each
#' sample.}
#' \item{n}{The number of samples.}
#' \item{q}{The number of variables after the data transformation. q is equal
#' to p.}
#' \item{x}{If \code{includes_transformed_data} is \code{TRUE}, then the
#' transformed data are included.}
#'
#' @references
#' Taguchi, G. (1995). Pattern Recognition and Quality Engineering (1).
#' \emph{Journal of Quality Engineering Society, 3}(2), 2-5. (In Japanese)
#'
#' Taguchi, G., Wu, Y., & Chodhury, S. (2000).
#' \emph{Mahalanobis-Taguchi System.} McGraw-Hill Professional.
#'
#' Taguchi, G., & Jugulum, R. (2002). \emph{The Mahalanobis-Taguchi strategy:
#' A pattern technology system.} John Wiley & Sons.
#'
#' Woodall, W. H., Koudelik, R., Tsui, K. L., Kim, S. B., Stoumbos, Z. G., &
#' Carvounis, C. P. (2003). A review and analysis of the Mahalanobis-Taguchi
#' system. \emph{Technometrics, 45}(1), 1-15.
#'
#' @seealso \code{\link[base]{solve}}, \code{\link{general_MT}},
#' \code{\link{generates_normalization_function}}, and
#' \code{\link{diagnosis.MT}}
#'
#' @examples
#' # 40 data for versicolor in the iris dataset
#' iris_versicolor <- iris[61:100, -5]
#'
#' unit_space_MT <- MT(unit_space_data = iris_versicolor,
#' includes_transformed_data = TRUE)
#'
#' # The following tol is a parameter passed to solve function.
#' unit_space_MT <- MT(unit_space_data = iris_versicolor,
#' includes_transformed_data = TRUE,
#' tol = 1e-9)
#'
#' (unit_space_MT$distance)
#'
#' @importFrom stats cor
#' @export
MT <- function(unit_space_data, includes_transformed_data = FALSE, ...) {
object_MT <- general_MT(unit_space_data = unit_space_data,
calc_A = function(x) solve(cor(x), ...),
generates_transform_function =
generates_normalization_function,
includes_transformed_data = includes_transformed_data)
class(object_MT) <- "MT"
return(object_MT)
}
#' Diagnosis method for the Mahalanobis-Taguchi (MT) method
#'
#' \code{diagnosis.MT} (via \code{\link{diagnosis}}) calculates the
#' mahalanobis distance based on the unit space generated by \code{\link{MT}}
#' or \code{\link{generates_unit_space}}(..., method = "MT") and classifies
#' each sample into positive (\code{TRUE}) or negative (\code{FALSE}) by
#' comparing the values with the set threshold value.
#'
#' @param unit_space Object of class "MT" generated by \code{\link{MT}} or
#' \code{\link{generates_unit_space}}(..., method = "MT").
#' @param newdata Matrix with n rows (samples) and p columns (variables). The
#' data are used to calculate the desired distances from the
#' unit space. All data should be continuous values and should
#' not have missing values.
#' @param threshold Numeric specifying the threshold value to classify each
#' sample into positive (\code{TRUE}) or negative
#' (\code{FALSE}).
#' @param includes_transformed_newdata If \code{TRUE}, then the transformed data
#' for \code{newdata} are included in a
#' return object.
#'
#' @return \code{diagnosis.MT} (via \code{\link{diagnosis}}) returns a list
#' containing the following components:
#'
#' \item{distance}{Vector with length n. Distances from the unit space to each
#' sample.}
#' \item{le_threshold}{Vector with length n. Logical values indicating the
#' distance of each sample is less than or equal to the
#' threhold value (\code{TRUE}) or not (\code{FALSE}).}
#' \item{threshold}{Numeric value to classify the sample into positive or
#' negative.}
#' \item{unit_space}{Object of class "MT" passed by \code{unit_space}.}
#' \item{n}{The number of samples for \code{newdata}.}
#' \item{q}{The number of variables after the data transformation. q equals p.}
#' \item{x}{If \code{includes_transformed_newdata} is \code{TRUE}, then the
#' transformed data for \code{newdata} are included.}
#'
#' @references
#' Taguchi, G. (1995). Pattern Recognition and Quality Engineering (1).
#' \emph{Journal of Quality Engineering Society, 3}(2), 2-5. (In Japanese)
#'
#' Taguchi, G., Wu, Y., & Chodhury, S. (2000).
#' \emph{Mahalanobis-Taguchi System.} McGraw-Hill Professional.
#'
#' Taguchi, G., & Jugulum, R. (2002). \emph{The Mahalanobis-Taguchi strategy:
#' A pattern technology system.} John Wiley & Sons.
#'
#' Woodall, W. H., Koudelik, R., Tsui, K. L., Kim, S. B., Stoumbos, Z. G., &
#' Carvounis, C. P. (2003). A review and analysis of the Mahalanobis-Taguchi
#' system. \emph{Technometrics, 45}(1), 1-15.
#'
#' @seealso \code{\link{general_diagnosis.MT}} and \code{\link{MT}}
#'
#' @examples
#' # 40 data for versicolor in the iris dataset
#' iris_versicolor <- iris[61:100, -5]
#'
#' unit_space_MT <- MT(unit_space_data = iris_versicolor,
#' includes_transformed_data = TRUE)
#'
#' # 10 data for each kind (setosa, versicolor, virginica) in the iris dataset
#' iris_test <- iris[c(1:10, 51:60, 101:111), -5]
#'
#' diagnosis_MT <- diagnosis(unit_space = unit_space_MT,
#' newdata = iris_test,
#' threshold = 4,
#' includes_transformed_newdata = TRUE)
#'
#' (diagnosis_MT$distance)
#' (diagnosis_MT$le_threshold)
#'
#' @export
diagnosis.MT <- function(unit_space,
newdata,
threshold = 4,
includes_transformed_newdata = FALSE) {
if (!inherits(unit_space, "MT")) {
warning("calling diagnosis.MT(<fake-MT-object>) ...")
}
general_diagnosis.MT(unit_space = unit_space,
newdata = newdata,
threshold = threshold,
includes_transformed_newdata =
includes_transformed_newdata)
}
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