R/v1_feature_LSCORE.R

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

#' Laplacian Score
#'
#' Laplacian Score \insertCite{he_laplacian_2005}{Rdimtools} is an unsupervised linear feature extraction method. For each
#' feature/variable, it computes Laplacian score based on an observation that data from the
#' same class are often close to each other. Its power of locality preserving property is used, and
#' the algorithm selects variables with smallest scores.
#'
#' @examples
#' \donttest{
#' ## use iris data
#' ## it is known that feature 3 and 4 are more important.
#' data(iris)
#' set.seed(100)
#' subid    <- sample(1:150, 50)
#' iris.dat <- as.matrix(iris[subid,1:4])
#' iris.lab <- as.factor(iris[subid,5])
#'
#' ## try different kernel bandwidth
#' out1 = do.lscore(iris.dat, t=0.1)
#' out2 = do.lscore(iris.dat, t=1)
#' out3 = do.lscore(iris.dat, t=10)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, pch=19, col=iris.lab, main="bandwidth=0.1")
#' plot(out2$Y, pch=19, col=iris.lab, main="bandwidth=1")
#' plot(out3$Y, pch=19, col=iris.lab, main="bandwidth=10")
#' par(opar)
#' }
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations
#' and columns represent independent variables.
#' @param ndim an integer-valued target dimension (default: 2).
#' @param ... extra parameters including \describe{
#' \item{preprocess}{an additional option for preprocessing the data.
#' See also \code{\link{aux.preprocess}} for more details (default: \code{"null"}).}
#' \item{type}{a vector of neighborhood graph construction. Following types are supported;
#' \code{c("knn",k)}, \code{c("enn",radius)}, and \code{c("proportion",ratio)}.
#' See also \code{\link{aux.graphnbd}} for more details (default: \code{c("proportion",0.1)}).}
#' \item{t}{bandwidth parameter for heat kernel in \eqn{(0,\infty)} (default: \code{1}).}
#' }
#'
#' @return a named \code{Rdimtools} S3 object containing
#' \describe{
#' \item{Y}{an \eqn{(n\times ndim)} matrix whose rows are embedded observations.}
#' \item{lscore}{a length-\eqn{p} vector of laplacian scores. Indices with smallest values are selected.}
#' \item{featidx}{a length-\eqn{ndim} vector of indices with highest scores.}
#' \item{projection}{a \eqn{(p\times ndim)} whose columns are basis for projection.}
#' \item{trfinfo}{a list containing information for out-of-sample prediction.}
#' \item{algorithm}{name of the algorithm.}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @rdname feature_LSCORE
#' @author Kisung You
#' @concept feature_methods
#' @export
do.lscore <- function(X, ndim=2, ...){
  #------------------------------------------------------------------------
  # INPUT : EXPLICIT
  # data matrix
  aux.typecheck(X)
  n = nrow(X)
  p = ncol(X)

  # ndim
  ndim = as.integer(ndim)
  if (!check_ndim(ndim,p)){
    stop("* do.lscore : 'ndim' is a positive integer in [1,#(covariates)].")
  }

  # INPUT : IMPLICIT
  params = list(...)
  pnames = names(params)

  # implicit 1. preprocessing
  if ("preprocess"%in%pnames){
    par_preprocess = tolower(params$preprocess)
  } else {
    par_preprocess = "null"
  }

  # implicit 2. neighborhood graph
  if ("type"%in%pnames){
    par_type = params$type
  } else {
    par_type = c("proportion",0.1)
  }
  par_symmetric = "union"

  # implicit 3. heat kernel
  if ("t"%in%pnames){
    par_t = as.double(params$t)
    if (!check_NumMM(par_t, 1e-15, Inf, compact=TRUE)){
      stop("* do.lscore : 't' is a kernel bandwidth parameter in (0,Inf).")
    }
  } else {
    par_t = 1.0
  }

  #------------------------------------------------------------------------
  # COMPUTATION : PRELIMINARY
  # 1. preprocessing
  tmplist = aux.preprocess.hidden(X, type=par_preprocess, algtype="linear")
  trfinfo = tmplist$info
  pX      = tmplist$pX

  # 2. neighborhood graph
  nbdstruct = aux.graphnbd(pX,
                           method="euclidean",
                           type=par_type,
                           symmetric=par_symmetric)
  nbdmask   = nbdstruct$mask

  #------------------------------------------------------------------------
  ## COMPUTATION : MAIN PART FOR LAPLACIAN SCORE
  #   1. weight matrix
  Dsqmat  = exp(-(as.matrix(dist(pX))^2)/par_t)
  S       = Dsqmat*nbdmask
  diag(S) = 0
  #   2. auxiliary matrices
  D = diag(rowSums(S))
  L = D-S
  #   3. compute Laplacian score
  n1 = as.vector(rep(1,n))
  D1 = as.vector(D%*%matrix(rep(1,n)))
  fscore = rep(0,p)
  for (j in 1:p){
    # 3-1. select each feature
    fr = as.vector(pX[,j])
    # 3-2. adjust fr
    corrector  = as.double(sum(fr*D1)/sum(n1*D1))
    frtilde    = fr-corrector
    matfrtilde = matrix(frtilde)
    # 3-3. compute the score
    term1 = sum(as.vector(L%*%matfrtilde)*frtilde)
    term2 = sum(as.vector(D%*%matfrtilde)*frtilde)
    fscore[j] = term1/term2
  }
  #   4. select the smallest ones
  idxvec = base::order(fscore, decreasing=FALSE)[1:ndim]
  #   5. find the projection matrix
  projection = aux.featureindicator(p,ndim,idxvec)

  #------------------------------------------------------------------------
  ## RETURN
  result = list()
  result$Y = pX%*%projection
  result$lscore  = fscore
  result$featidx = idxvec
  result$projection = projection
  result$trfinfo    = trfinfo
  result$algorithm  = "linear:LSCORE"
  return(structure(result, class="Rdimtools"))
}