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#' Interactive Document Map
#'
#' Interactive Document Map originates from text analysis to generate maps of documents by placing
#' similar documents in the same neighborhood. After defining pairwise distance with cosine similarity,
#' authors asserted to use either \code{NNP} or \code{FastMap} as an engine behind.
#'
#' @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.
#' @param preprocess an additional option for preprocessing the data.
#' Default is "null". See also \code{\link{aux.preprocess}} for more details.
#' @param engine either \code{NNP} or \code{FastMap}.
#'
#' @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.}
#' }
#'
#' @examples
#' \donttest{
#' ## load iris data
#' data(iris)
#' set.seed(100)
#' subid = sample(1:150,50)
#' X = as.matrix(iris[subid,1:4])
#' lab = as.factor(iris[subid,5])
#'
#' ## let's compare with other methods
#' out1 <- do.pca(X, ndim=2)
#' out2 <- do.lda(X, ndim=2, label=lab)
#' out3 <- do.idmap(X, ndim=2, engine="NNP")
#'
#' ## visualize
#' opar <- par(no.readonly=TRUE)
#' par(mfrow=c(1,3))
#' plot(out1$Y, pch=19, col=lab, main="PCA")
#' plot(out2$Y, pch=19, col=lab, main="LDA")
#' plot(out3$Y, pch=19, col=lab, main="IDMAP")
#' par(opar)
#' }
#'
#' @references
#' \insertRef{minghim_contentbased_2006}{Rdimtools}
#'
#' @seealso \code{\link{do.nnp}}, \code{\link{do.fastmap}}
#' @rdname nonlinear_IDMAP
#' @concept nonlinear_methods
#' @export
do.idmap <- function(X, ndim=2, preprocess=c("null","center","scale","cscale","whiten","decorrelate"), engine=c("NNP","FastMap")){
########################################################################
## 1. Type Checking
aux.typecheck(X)
n = nrow(X)
p = ncol(X)
ndim = as.integer(ndim)
if (!check_ndim(ndim,p)){stop("* do.idmap : 'ndim' is a positive integer in [1,#(covariates)).")}
algpreprocess = match.arg(preprocess)
########################################################################
## 2. Preprocessing
tmplist = (X,type=algpreprocess,algtype="nonlinear")
trfinfo = tmplist$info
pX = tmplist$pX
########################################################################
## 3. Preliminary Computation of Cosine Similarity
D = array(0,c(n,n))
for (i in 1:n){
D[i,i] = 0
}
for (i in 1:(n-1)){
ti = as.vector(pX[i,])
for (j in (i+1):n){
tj = as.vector(pX[j,])
scos = sum(ti*tj)/sqrt(sum(ti^2)*sum(tj^2))
theval = sqrt(2*(1-scos))
D[i,j] = theval
D[j,i] = theval
}
}
########################################################################
## 4. typechecking
if (missing(engine)){
engine = "NNP"
} else {
engine = match.arg(engine)
}
if (engine=="FastMap"){
k=ndim
Dold=D
Dnew = array(0,c(n,n))
output = array(0,c(n,ndim))
for (i in 1:k){
# 3-1. find row and column index for maximal element
maxidx = aux.findmaxidx(Dold)
ida = maxidx[1]
idb = maxidx[2]
# 3-2. precompute some values
dab2 = (sum(as.vector(pX[ida,]-pX[idb,])^2))
if (dab2 > (sqrt(123*.Machine$double.eps))){
dab = sqrt(dab2)
# 3-3. compute coefficient
for (j in 1:n){
output[j,i] = (sum(as.vector(pX[ida,]-pX[j,])^2) + dab2 - sum(as.vector(pX[idb,]-pX[j,])^2))/(2*dab)
}
} # or, leave it as zero
# 3-4. update D : compute and alter
for (it1 in 1:n){
for (it2 in 1:n){
Dnew[it1,it2] = sqrt((Dold[it1,it2]^2) - ((output[it1,i]-output[it2,i])^2))
}
}
Dold = Dnew
}
result = list()
result$Y = output
trfinfo$algtype = "nonlinear"
result$trfinfo = trfinfo
} else if (engine=="NNP"){ #######-----------------------################
included = rep(FALSE, n)
pY = array(0,c(n,ndim))
initid = aux.findmaxidx(D)
initQ = as.integer(initid[1]) # two farthest points
initR = as.integer(initid[2])
included[initid] = TRUE # adjust included ones
pY[initQ,] = c(D[initQ,initR]/2, rep(0,(ndim-1)))
pY[initR,] = c(-D[initQ,initR]/2, rep(0,(ndim-1)))
toberun = setdiff(1:n, initid)
# for general case, I'm using this.
minfunc <- function(z,center1,center2,rad1,rad2){
return(abs(sqrt(sum((z-center1)^2))-rad1)+abs(sqrt(sum((z-center2)^2))-rad2))
}
Dctrl = RcppDE::DEoptim.control(trace=FALSE)
bdlower = rep(-D[initQ,initR], ndim)
bdupper = rep(D[initQ,initR], ndim)
## 4. Main Iteration
for (i in 1:length(toberun)){
# 4-1. current index
idx = toberun[i]
# 4-2. find two nearest ones
currentincluded = which(included) # index for currently available ones
if (length(currentincluded)==2){
idq = currentincluded[1]
idr = currentincluded[2]
} else {
currentdist = D[idx,currentincluded]
bottom2 = currentdist[order(currentdist)[1:3]]
idq = currentincluded[(currentdist==bottom2[2])]
idr = currentincluded[(currentdist==bottom2[3])]
if (length(idq)>1){
idq = as.integer(idq[1])
}
if (length(idr)>1){
idr = as.integer(idr[1])
}
}
# 4-3. get ready for distances
dxq = as.double(D[idx,idq])
dxr = as.double(D[idx,idr])
dxsum = (dxq+dxr)
dqrlow = sqrt(sum(as.vector(pY[idq,]-pY[idr,])^2))
# 4-4. type branching
q = as.vector(pY[idq,])
r = as.vector(pY[idr,])
if (dxsum==dqrlow){
pY[idx,] = ((r-q)*dxq/(dxq+dxr))+q
} else if (dxsum>dqrlow){
runDEoptim = RcppDE::DEoptim(minfunc, lower=bdlower, upper=bdupper, control=Dctrl, center1=q, center2=r, rad1=dxq, rad2=dxr)
pY[idx,] = as.vector((runDEoptim$optim$bestmem))
} else { # now, we have two cases
if (dxq<dxr){
pY[idx,] = q+((r-q)*0.5)
} else {
pY[idx,] = r+((q-r)*0.5)
}
}
# 4-5. update index
included[idx] = TRUE
}
result = list()
result$Y = pY
trfinfo$algtype = "nonlinear"
result$trfinfo = trfinfo
}
########################################################################
## 5. return output
return(result)
}
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