#' Semi-Supervised Locally Discriminant Projection
#'
#' Semi-Supervised Locally Discriminant Projection (SSLDP) is a semi-supervised
#' extension of LDP. It utilizes unlabeled data to overcome the small-sample-size problem
#' under the situation where labeled data have the small number. Using two information,
#' it both constructs the within- and between-class weight matrices incorporating the
#' neighborhood information of the data set.
#'
#' @examples
#' ## use iris data
#' data(iris)
#' X = as.matrix(iris[,1:4])
#' label = as.integer(iris$Species)
#'
#' ## copy a label and let 10% of elements be missing
#' nlabel = length(label)
#' nmissing = round(nlabel*0.10)
#' label_missing = label
#' label_missing[sample(1:nlabel, nmissing)]=NA
#'
#' ## compute with 3 different levels of 'beta' values
#' out1 = do.ssldp(X, label_missing, beta=0.1)
#' out2 = do.ssldp(X, label_missing, beta=0.5)
#' out3 = do.ssldp(X, label_missing, beta=0.9)
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, col=label, main="SSLDP::beta=0.1")
#' plot(out2$Y, col=label, main="SSLDP::beta=0.5")
#' plot(out3$Y, col=label, main="SSLDP::beta=0.9")
#' par(opar)
#'
#' @param X an \eqn{(n\times p)} matrix or data frame whose rows are observations
#' and columns represent independent variables.
#' @param label a length-\eqn{n} vector of data class labels.
#' @param ndim an integer-valued target dimension.
#' @param type a vector of neighborhood graph construction. Following types are supported;
#' \code{c("knn",k)}, \code{c("enn",radius)}, and \code{c("proportion",ratio)}.
#' Default is \code{c("proportion",0.1)}, connecting about 1/10 of nearest data points
#' among all data points. See also \code{\link{aux.graphnbd}} for more details.
#' @param preprocess an additional option for preprocessing the data.
#' Default is "center". See also \code{\link{aux.preprocess}} for more details.
#' @param beta balancing parameter for intra- and inter-class information in \eqn{[0,1]}.
#'
#' @return a named list containing
#' \describe{
#' \item{Y}{an \eqn{(n\times ndim)} matrix whose rows are embedded observations.}
#' \item{trfinfo}{a list containing information for out-of-sample prediction.}
#' \item{projection}{a \eqn{(p\times ndim)} whose columns are basis for projection.}
#' }
#'
#' @references
#' \insertRef{zhang_semisupervised_2011}{Rdimtools}
#'
#' @author Kisung You
#' @rdname linear_SSLDP
#' @concept linear_methods
#' @export
do.ssldp <- function(X, label, ndim=2, type=c("proportion",0.1),
preprocess=c("center","scale","cscale","whiten","decorrelate"), beta=0.5){
#------------------------------------------------------------------------
## PREPROCESSING
# 1. data matrix
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
# 2. label : check and return a de-factored vector
# For this example, there should be no degenerate class of size 1.
label = check_label(label, n)
ulabel = unique(label)
if (all(!is.na(ulabel))){
message("* Semi-Supervised Learning : there is no missing labels. Consider using Supervised methods.")
}
if (any(is.infinite(ulabel))){
stop("* Semi-Supervised Learning : no label of Inf is allowed.")
}
# 3. ndim
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){stop("* do.ssldp : 'ndim' is a positive integer in [1,#(covariates)).")}
# 4. neighborhood information : asymmetric
nbdtype = type
nbdsymmetric = "union"
# 5. preprocess
if (missing(preprocess)){
algpreprocess = "center"
} else {
algpreprocess = match.arg(preprocess)
}
# 6. beta
beta = as.double(beta)
if (!check_NumMM(beta,0,1,compact=TRUE)){stop("* do.ssldp : 'beta' is a balancing parameter in [0,1].")}
#------------------------------------------------------------------------
## COMPUTATION : PRELIMINARY
# 1. preprocessing of data : note that output pX still has (n-by-p) format
tmplist = (X,type=algpreprocess,algtype="linear")
trfinfo = tmplist$info
pX = tmplist$pX
# 2. build neighborhood information
nbdstruct = aux.graphnbd(pX,method="euclidean",
type=nbdtype,symmetric=nbdsymmetric)
nbdmask = nbdstruct$mask
# 3. compute norm for squared difference norms and one's norms
matDsq = (as.matrix(dist(pX))^2)
vecnom = rep(0,n)
for (i in 1:n){
thevector = as.vector(pX[i,])
vecnom[i] = sqrt(sum(thevector*thevector))
}
# 4. number of classes
C = length(setdiff(ulabel,NA))
#------------------------------------------------------------------------
## COMPUTATION : MAIN PART FOR SEMI-SUPERVISED LDP
# 1. build weight matrices
Hw = array(0,c(n,n))
Hb = array(0,c(n,n))
for (i in 1:(n-1)){
class1 = label[i]
for (j in (i+1):n){
class2 = label[j]
# 1-1. within-class weight
if ((nbdmask[i,j]==TRUE)||(nbdmask[j,i]==TRUE)){
if (((!is.na(class1))&&(!is.na(class2)))&&(class1==class2)){
thevalue = exp(-((matDsq[i,j])/(vecnom[i]*vecnom[j])))
Hw[i,j] = thevalue
Hw[j,i] = thevalue
} else if (is.na(class1)||is.na(class2)){
thevalue = exp(-((matDsq[i,j])/(vecnom[i]*vecnom[j])))/C
Hw[i,j] = thevalue
Hw[j,i] = thevalue
} else if (is.na(class1)&&is.na(class2)){
thevalue = exp(-((matDsq[i,j])/(vecnom[i]*vecnom[j])))/(C^2)
Hw[i,j] = thevalue
Hw[j,i] = thevalue
}
# 1-2. between-class weight
if (((!is.na(class1))&&(!is.na(class2)))&&(class1!=class2)){
thevalue = exp(-((matDsq[i,j])/(vecnom[i]*vecnom[j])))
Hb[i,j] = thevalue
Hb[j,i] = thevalue
}
}
}
}
# 2. build auxiliary matrices
Dw = diag(rowSums(Hw))
Lb = diag(rowSums(Hb))-Hb
# 3. build cost functions
LHS = t(pX)%*%(Lb-beta*Hw)%*%pX
RHS = t(pX)%*%Dw%*%pX
# 4. find projection : use top eigenvectors for geigen problem
projection = aux.geigen(LHS, RHS, ndim, maximal=TRUE)
#------------------------------------------------------------------------
## RETURN
result = list()
result$Y = pX%*%projection
result$trfinfo = trfinfo
result$projection = projection
return(result)
}
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