R/s_TLS.R

In egenn/rtemis: Machine Learning and Visualization

# s_TLS.R
# ::rtemis::
# 2015 E.D. Gennatas www.lambdamd.org

#' Total Least Squares Regression \[R\]
#'
#' A minimal function to perform total least squares regression
#'
#' The main differences between a linear model and TLS is that the latter assumes
#' error in the features as well as the outcome. The solution is essentially the
#' projection on the first principal axis.
#'
#' @inheritParams s_GLM
#' @author E.D. Gennatas
#' @export

s_TLS <- function(x, y = NULL,
                  x.test = NULL, y.test = NULL,
                  x.name = "x", y.name = "y",
                  print.plot = FALSE,
                  plot.fitted = NULL,
                  plot.predicted = NULL,
                  plot.theme = rtTheme,
                  question = NULL,
                  verbose = TRUE,
                  outdir = NULL,
                  save.mod = ifelse(!is.null(outdir), TRUE, FALSE), ...) {
  # Intro ----
  if (missing(x)) {
    print(args(s_TLS))
    return(invisible(9))
  }
  if (!is.null(outdir)) outdir <- normalizePath(outdir, mustWork = FALSE)
  logFile <- if (!is.null(outdir)) {
    paste0(
      outdir, "/", sys.calls()[[1]][[1]], ".",
      format(Sys.time(), "%Y%m%d.%H%M%S"), ".log"
    )
  } else {
    NULL
  }
  start.time <- intro(verbose = verbose, logFile = logFile)
  mod.name <- "TLS"

  # Arguments ----
  if (missing(x)) {
    print(args(s_TLS))
    stop("x is missing")
  }
  if (is.null(y) && NCOL(x) < 2) {
    print(args(s_TLS))
    stop("y is missing")
  }
  if (is.null(x.name)) x.name <- getName(x, "x")
  if (is.null(y.name)) y.name <- getName(y, "y")
  if (!verbose) print.plot <- FALSE
  verbose <- verbose || !is.null(logFile)
  if (save.mod && is.null(outdir)) outdir <- paste0("./s.", mod.name)
  if (!is.null(outdir)) outdir <- paste0(normalizePath(outdir, mustWork = FALSE), "/")

  # Data ----
  dt <- prepare_data(x, y, x.test, y.test)
  x <- dt$x
  y <- dt$y
  x.test <- dt$x.test
  y.test <- dt$y.test
  xnames <- dt$xnames
  type <- dt$type
  checkType(type, "Regression", mod.name)
  if (verbose) dataSummary(x, y, x.test, y.test, type)
  if (print.plot) {
    if (is.null(plot.fitted)) plot.fitted <- if (is.null(y.test)) TRUE else FALSE
    if (is.null(plot.predicted)) plot.predicted <- if (!is.null(y.test)) TRUE else FALSE
  } else {
    plot.fitted <- plot.predicted <- FALSE
  }

  # TLS ----
  if (verbose) msg2("Running Total Least Squares...", newline.pre = TRUE)
  M <- cbind(as.matrix(x), y)
  m <- NROW(x)
  n <- NCOL(x)
  M.mean <- matrix(rep(apply(M, 2, mean), m), nrow = m, byrow = TRUE)
  colnames(M.mean) <- c(colnames(x), "y")

  # '- SVD ----
  M.svd <- svd(M - M.mean)
  V <- M.svd$v
  a <- -V[1:n, n + 1] / V[n + 1, n + 1]
  b <- mean(M %*% V[, n + 1]) / V[n + 1, n + 1]
  mod <- list(a = a, b = b)
  class(mod) <- c("rtTLS", "list")

  # Fitted ----
  fitted <- c(cbind(as.matrix(x), 1) %*% c(a, b))
  normal <- V[, n + 1]
  error <- abs((M - M.mean) %*% normal)
  ssq <- sum(error^2)
  error.train <- mod_error(y, fitted)
  if (verbose) errorSummary(error.train, mod.name)

  # Predicted ----
  predicted <- error.test <- NULL
  if (!is.null(x.test)) {
    predicted <- c(cbind(as.matrix(x.test), 1) %*% c(a, b))
    if (!is.null(y.test)) {
      error.test <- mod_error(y.test, predicted)
      if (verbose) errorSummary(error.test, mod.name)
    }
  }

  # Outro ----
  rt <- rtModSet(
    rtclass = "rtMod",
    mod = mod,
    mod.name = mod.name,
    type = type,
    y.train = y,
    y.test = y.test,
    x.name = x.name,
    y.name = y.name,
    xnames = xnames,
    fitted = fitted,
    se.fit = NULL,
    error.train = error.train,
    predicted = predicted,
    se.prediction = NULL,
    error.test = error.test,
    question = question,
    extra = list(M = M, M.svd = M.svd, a = a, b = b, error = error, ssq = ssq)
  )

  rtMod.out(
    rt,
    print.plot,
    plot.fitted,
    plot.predicted,
    y.test,
    mod.name,
    outdir,
    save.mod,
    verbose,
    plot.theme
  )

  outro(start.time, verbose = verbose, sinkOff = ifelse(is.null(logFile), FALSE, TRUE))
  rt
} # rtemis::s_TLS


#' `predict.rtTLS`: `predict` method for `rtTLS` object
#'
#' @method predict rtTLS
#' @param object `rtTLS` object created by [s_TLS]
#' @param newdata `data.frame` of new data.
#' @param ... Not used.
#' 
#' @export
predict.rtTLS <- function(object, newdata, ...) {
  c(cbind(as.matrix(newdata), 1) %*% c(object$a, object$b))
} # rtemis::predict.rtTLS


#' `print.rtTLS`: `print` method for `rtTLS` object
#'
#' @method print rtTLS
#' @param x `rtTLS` object created by [s_TLS]
#' @param ... Not used.
#' 
#' @export
print.rtTLS <- function(x, ...) {
  cat("rtemis Total Least Squares Regression object (rtTLS)")
  invisible(x)
} # rtemis::print.rtTLS