R/tune.rcc.R

In mixOmics: Omics Data Integration Project

#' Estimate the parameters of regularization for Regularized CCA
#' 
#' Computes leave-one-out or M-fold cross-validation scores on a
#' two-dimensional grid to determine optimal values for the parameters of
#' regularization in \code{rcc}.
#' 
#' If \code{validation="Mfolds"}, M-fold cross-validation is performed by
#' calling \code{Mfold}. When \code{folds} is given, the elements of
#' \code{folds} should be integer vectors specifying the indices of the
#' validation sample and the argument \code{M} is ignored. Otherwise, the folds
#' are generated. The number of cross-validation folds is specified with the
#' argument \code{M}.
#' 
#' If \code{validation="loo"}, leave-one-out cross-validation is performed by
#' calling the \code{loo} function. In this case the arguments \code{folds} and
#' \code{M} are ignored.
#' 
#' The estimation of the missing values can be performed by the reconstitution
#' of the data matrix using the \code{nipals} function. Otherwise, missing
#' values are handled by casewise deletion in the \code{rcc} function.
#' 
#' @param X numeric matrix or data frame \eqn{(n \times p)}, the observations
#' on the \eqn{X} variables. \code{NA}s are allowed.
#' @param Y numeric matrix or data frame \eqn{(n \times q)}, the observations
#' on the \eqn{Y} variables. \code{NA}s are allowed.
#' @param grid1,grid2 vector numeric defining the values of \code{lambda1} and
#' \code{lambda2} at which cross-validation score should be computed. Defaults
#' to \code{grid1=grid2=seq(0.001, 1, length=5)}.
#' @param validation character string. What kind of (internal) cross-validation
#' method to use, (partially) matching one of \code{"loo"} (leave-one-out) or
#' \code{"Mfolds"} (M-folds). See Details.
#' @param folds positive integer. Number of folds to use if
#' \code{validation="Mfold"}. Defaults to \code{folds=10}.
#' @param plot logical argument indicating whether a image map should be
#' plotted by calling the \code{imgCV} function.
#' @return The returned value is a list with components: \item{opt.lambda1,}{}
#' \item{opt.lambda2}{value of the parameters of regularization on which the
#' cross-validation method reached it optimal.} \item{opt.score}{the optimal
#' cross-validation score reached on the grid.} \item{grid1, grid2}{original
#' vectors \code{grid1} and \code{grid2}.} \item{mat}{matrix containing the
#' cross-validation score computed on the grid.}
#' @author Sébastien Déjean, Ignacio González, Kim-Anh Lê Cao, Al J Abadi
#' @seealso \code{\link{image.tune.rcc}} and http://www.mixOmics.org for more
#' details.
#' @keywords multivariate dplot
#' @export
#' @examples
#' data(nutrimouse)
#' X <- nutrimouse$lipid
#' Y <- nutrimouse$gene
#' 
#' ## this can take some seconds
#' 
#' tune.rcc(X, Y, validation = "Mfold")
tune.rcc <-
    function(X, 
             Y, 
             grid1 = seq(0.001, 1, length = 5), 
             grid2 = seq(0.001, 1, length = 5), 
             validation = c("loo", "Mfold"), 
             folds = 10,
             plot = TRUE)
    {
        
        # validation des arguments #
        #--------------------------#
        if (length(dim(X)) != 2 || length(dim(Y)) != 2) 
            stop("'X' and/or 'Y' must be a numeric matrix.")
        
        X = as.matrix(X)
        Y = as.matrix(Y)
        
        if (!is.numeric(X) || !is.numeric(Y)) 
            stop("'X' and/or 'Y' must be a numeric matrix.")
        
        if (nrow(X) != nrow(Y)) 
            stop("unequal number of rows in 'X' and 'Y'.")
        
        validation = match.arg(validation)
        grid = expand.grid(grid1, grid2)
        
        if (validation == "loo")
        {
            M = nrow(X)
            folds = split(1:M, 1:M)
            cv.score = apply(grid, 1, function(lambda)
            {
                Mfold(X, Y, lambda[1], lambda[2], folds)
            })
            
        } else {
            nr = nrow(X)
            M = length(folds)
            if (is.null(folds) || !is.numeric(folds) || folds < 2 || folds > nr)
            {
                stop("Invalid number of folds.")
            } else {
                M = round(folds)
                folds = split(sample(1:nr), rep(1:M, length = nr))
            }
            cv.score = apply(grid, 1, function(lambda) 
            {
                Mfold(X, Y, lambda[1], lambda[2], folds)
            })
        }
        
        cv.score.grid = cbind(grid, cv.score)
        mat = matrix(cv.score, nrow = length(grid1), ncol = length(grid2))
        
        if (isTRUE(plot))
            image.tune.rcc(list(grid1 = grid1, grid2 = grid2, mat = mat))
        
        opt = cv.score.grid[cv.score.grid[, 3] == max(cv.score.grid[, 3]), ]
        #cat("  lambda1 = ", opt[[1]], "\n", " lambda2 = ", opt[[2]], "\n",
        #"CV-score = ", opt[[3]], "\n")
        
        out = list(opt.lambda1 = opt[[1]], opt.lambda2 = opt[[2]], 
                   opt.score = opt[[3]], grid1 = grid1, grid2 = grid2, mat = mat)
        
        out$call = match.call()
        
        class(out) = "tune.rcc"
        return(invisible(out))
    }


Mfold = function(X, Y, lambda1, lambda2, folds)
{
    
    xscore = NULL
    yscore = NULL
    M = length(folds)
    
    for (m in 1:M)
    {
        omit = folds[[m]]
        result = rcc(X[-omit, , drop = FALSE], Y[-omit, , drop = FALSE], ncomp = 1, lambda1, lambda2, method = "ridge")
        X[omit, ][is.na(X[omit, ])] = 0
        Y[omit, ][is.na(Y[omit, ])] = 0
        xscore = c(xscore, X[omit, , drop = FALSE] %*% result$loadings$X[, 1])
        yscore = c(yscore, Y[omit, , drop = FALSE] %*% result$loadings$Y[, 1])
    }
    
    cv.score = cor(xscore, yscore, use = "pairwise")
    return(invisible(cv.score))
}