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#' Supervised classification using quadratic discriminant analysis
#'
#' @description
#' Unified (formula-based) interface version of the quadratic discriminant
#' analysis algorithm provided by [MASS::qda()].
#'
#' @param formula a formula with left term being the factor variable to predict
#' and the right term with the list of independent, predictive variables,
#' separated with a plus sign. If the data frame provided contains only the
#' dependent and independent variables, one can use the `class ~ .` short
#' version (that one is strongly encouraged). Variables with minus sign are
#' eliminated. Calculations on variables are possible according to usual
#' formula convention (possibly protected by using `I()`).
#' @param data a data.frame to use as a training set.
#' @param train a matrix or data frame with predictors.
#' @param response a vector of factor for the classification.
#' @param ... further arguments passed to [MASS::qda()] or its [predict()]
#' method (see the corresponding help page).
#' @param subset index vector with the cases to define the training set in use
#' (this argument must be named, if provided).
#' @param na.action function to specify the action to be taken if `NA`s are
#' found. For [ml_qda()] `na.fail` is used by default. The calculation is
#' stopped if there is any `NA` in the data. Another option is `na.omit`,
#' where cases with missing values on any required variable are dropped (this
#' argument must be named, if provided). For the `predict()` method, the
#' default, and most suitable option, is `na.exclude`. In that case, rows with
#' `NA`s in `newdata=` are excluded from prediction, but reinjected in the
#' final results so that the number of items is still the same (and in the
#' same order as `newdata=`).
#' @param object an **mlQda** object
#' @param newdata a new dataset with same conformation as the training set (same
#' variables, except may by the class for classification or dependent variable
#' for regression). Usually a test set, or a new dataset to be predicted.
#' @param type the type of prediction to return. `"class"` by default, the
#' predicted classes. Other options are `"membership"` the membership (a
#' number between 0 and 1) to the different classes, or `"both"` to return
#' classes and memberships.
#' @param prior the prior probabilities of class membership. By default, the
#' prior are obtained from the object and, if they where not changed,
#' correspond to the proportions observed in the training set.
#' @param method `"plug-in"`, `"predictive"`, `"debiased"`, `"looCV"`, or
#' `"cv"`. `"plug-in"` (default) the usual unbiased parameter estimates are
#' used. With `"predictive"`, the parameters are integrated out using a vague
#' prior. With `"debiased"`, an unbiased estimator of the log posterior
#' probabilities is used. With `"looCV"`, the leave-one-out cross-validation
#' fits to the original data set are computed and returned. With `"cv"`,
#' cross-validation is used instead. If you specify `method = "cv"` then
#' [cvpredict()] is used and you cannot provide `newdata=` in that case.
#'
#' @return [ml_qda()]/[mlQda()] creates an **mlQda**, **mlearning** object
#' containing the classifier and a lot of additional metadata used by the
#' functions and methods you can apply to it like [predict()] or
#' [cvpredict()]. In case you want to program new functions or extract
#' specific components, inspect the "unclassed" object using [unclass()].
#' @seealso [mlearning()], [cvpredict()], [confusion()], also [MASS::qda()] that
#' actually does the classification.
#' @export
#'
#' @examples
#' # Prepare data: split into training set (2/3) and test set (1/3)
#' data("iris", package = "datasets")
#' train <- c(1:34, 51:83, 101:133)
#' iris_train <- iris[train, ]
#' iris_test <- iris[-train, ]
#' # One case with missing data in train set, and another case in test set
#' iris_train[1, 1] <- NA
#' iris_test[25, 2] <- NA
#'
#' iris_qda <- ml_qda(data = iris_train, Species ~ .)
#' summary(iris_qda)
#' confusion(iris_qda)
#' confusion(predict(iris_qda, newdata = iris_test), iris_test$Species)
#'
#' # Another dataset (binary predictor... not optimal for qda, just for test)
#' data("HouseVotes84", package = "mlbench")
#' house_qda <- ml_qda(data = HouseVotes84, Class ~ ., na.action = na.omit)
#' summary(house_qda)
mlQda <- function(train, ...)
UseMethod("mlQda")
#' @rdname mlQda
#' @export
ml_qda <- mlQda
#' @rdname mlQda
#' @export
#' @method mlQda formula
mlQda.formula <- function(formula, data, ..., subset, na.action) {
mlearning(formula, data = data, method = "mlQda", model.args =
list(formula = formula, data = substitute(data),
subset = substitute(subset)), call = match.call(), ...,
subset = subset, na.action = substitute(na.action))
}
#' @rdname mlQda
#' @export
#' @method mlQda default
mlQda.default <- function(train, response, ...) {
if (!is.factor(response))
stop("only factor response (classification) accepted for mlQda")
dots <- list(...)
.args. <- dots$.args.
dots$.args. <- NULL
if (!length(.args.))
.args. <- list(levels = levels(response),
n = c(intial = NROW(train), final = NROW(train)),
type = "classification", na.action = "na.pass",
mlearning.call = match.call(), method = "mlQda")
# Check if there are factor predictors
if (any(sapply(train, is.factor)))
warning("force conversion from factor to numeric; may be not optimal or suitable")
# Return a mlearning object
structure(MASS::qda(x = sapply(train, as.numeric),
grouping = response, ...), formula = .args.$formula, train = train,
response = response, levels = .args.$levels, n = .args.$n, args = dots,
optim = .args.$optim, numeric.only = TRUE, type = .args.$type,
pred.type = c(class = "class", membership = "posterior"),
summary = NULL, na.action = .args.$na.action,
mlearning.call = .args.$mlearning.call, method = .args.$method,
algorithm = "quadratic discriminant analysis",
class = c("mlQda", "mlearning", "qda"))
}
#' @rdname mlQda
#' @export
#' @method predict mlQda
predict.mlQda <- function(object, newdata,
type = c("class", "membership", "both"), prior = object$prior,
method = c("plug-in", "predictive", "debiased", "looCV", "cv"), ...) {
if (!inherits(object, "mlQda"))
stop("'object' must be a 'mlQda' object")
# If method == "cv", delegate to cvpredict()
method <- as.character(method)[1]
if (method == "cv") {
if (!missing(newdata))
stop("cannot handle new data with method = 'cv'")
return(cvpredict(object = object, type = type, prior = prior, ...))
}
# Recalculate newdata according to formula...
if (missing(newdata)) {# Use train
newdata <- attr(object, "train")
} else if (attr(object, "optim")) {# Use optimized approach
# Just keep vars similar as in train
vars <- names(attr(object, "train"))
if (!all(vars %in% names(newdata)))
stop("One or more missing variables in newdata")
newdata <- newdata[, vars]
} else {# Use model.frame
# but eliminate dependent variable, not required
# (second item in the formula)
newdata <- model.frame(formula = attr(object, "formula")[-2],
data = newdata, na.action = na.pass)[, names(attr(object, "train"))]
}
# Only numerical predictors
newdata <- sapply(as.data.frame(newdata), as.numeric)
# Delegate to the MASS predict.qda method
class(object) <- class(object)[-(1:2)]
# I need to suppress warnings, because NAs produce ennoying warnings!
if (method == "looCV") {
res <- suppressWarnings(predict(object, prior = prior, method = method,
...))
} else {
res <- suppressWarnings(predict(object, newdata = newdata, prior = prior,
method = method, ...))
}
# Rework results according to what we want
switch(as.character(type)[1],
class = factor(as.character(res$class), levels = levels(object)),
membership = .membership(res$posterior, levels = levels(object)),
both = list(class = factor(as.character(res$class),
levels = levels(object)), membership = .membership(res$posterior,
levels = levels(object))),
stop("unrecognized 'type' (must be 'class', 'membership' or 'both')"))
}
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