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R/Parafac.R
In rrcov3way: Robust Methods for Multiway Data Analysis, Applicable also for Compositional Data
Defines functions
print.parafac
plot.parafac
.cutoff.sd
.cutoff.rd
Parafac
Documented in
Parafac
plot.parafac
print.parafac
Parafac <- function(X, ncomp=2,
center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "atld", "int2"),
robust=FALSE, coda.transform=c("none", "ilr", "clr"),
ncomp.rpca=0, alpha=0.75, robiter=100, crit=0.975, # arguments for the robust parafac
trace=FALSE)
{
call <- match.call()
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
if(optim == "atld" && robust)
stop("The robust option is not possible with 'atld' optimization. Please use 'als' or 'int2'.")
coda.transform <- match.arg(coda.transform)
ilr <- coda.transform != "none"
if(coda.transform == "clr" & robust)
stop("The robust option is not possible with 'clr' transform compositional data. Please use 'ilr'.")
if(length(crit) != 1 || crit <= 0 || crit >= 1)
stop("'crit' has to be a single positive number less than 1!")
if(crit < 0.5)
crit <- 1 - crit
stopifnot(alpha <= 1 & alpha >= 0.5)
ret <- if(robust & ilr) .Parafac.rob.ilr(X=X, ncomp=ncomp, # robust, compositional
center=center, center.mode=center.mode,
scale=scale, scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit,
coda.transform=coda.transform,
ncomp.rpca=ncomp.rpca, alpha=alpha, robiter=robiter,
trace=trace)
else if(!robust & !ilr) .Parafac(X=X, ncomp=ncomp, #
center=center, center.mode=center.mode, scale=scale,
scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit, optim=optim, trace=trace)
else if(!robust & ilr) .Parafac.ilr(X=X, ncomp=ncomp, # compositional
center=center, center.mode=center.mode,
scale=scale, scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit,
coda.transform=coda.transform,
trace=trace)
else if(robust & !ilr) .Parafac.rob(X=X, ncomp=ncomp, # robust
center=center, center.mode=center.mode,
scale=scale, scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit, optim=optim,
ncomp.rpca=ncomp.rpca, alpha=alpha, robiter=robiter,
trace=trace)
## Total sum of squares, PARAFAC fit and fit percentage:
## ret$ss <- sum(X^2)
## ret$fit will be ||X_A - A G_A kron(C',B')||^2 where X_A and G_A denote the matricized (frontal slices) data array and core array
## ret$fp is equal to: 100*(ss-ret$fit)/ss
## Calculate the superdiagonal core g_sss and store it in GA
ret$GA <- sqrt(colSums(ret$A^2)) * sqrt(colSums(ret$B^2)) * sqrt(colSums(ret$C^2))
names(ret$GA) <- colnames(ret$A)
ret$ncomp <- ncomp
ret$optim <- optim
ret$call <- call
ret
}
.cutoff.rd <- function(rd, h, crit=0.975, robust=TRUE)
{
if(robust)
{
## a) Using median and MAD
## ret <- (median(rd^(2/3)) + mad(rd^(2/3)) * qnorm(crit))^(3/2)
##
## b) Using MASS cov.mcd (will need to import - library(MASS))
## unimcd <- cov.mcd(rd^(2/3),quantile.used=h)
## ret <- sqrt(qnorm(0.975, unimcd$center, sqrt(unimcd$cov))^3)
##
## c) Using UNIMCD
unimcd <- rrcov:::unimcd(rd^(2/3), quan=h)
ret <- sqrt(qnorm(crit, unimcd$tmcd, unimcd$smcd)^3)
## d) Using UNIMCD by CovMcd
## unimcd <- CovMcd(rd, alpha=h/length(rd))
## ret <- sqrt(qnorm(crit, getCenter(unimcd), sqrt(getCov(unimcd)))^3)
##
} else
ret <- (mean(rd^(2/3)) + sd(rd^(2/3)) * qnorm(crit))^(3/2)
ret
}
.cutoff.sd <- function(A, alpha, crit, robust=TRUE)
{
if(robust)
{
## VT::24.04.2020 Workaround - PcaHubert with mcd=FALSE will crash if A is one-dimensional matrix.
## now this is fixed in rrcov
##
## pc <- PcaHubert(A, alpha=alpha, k=ncol(A), mcd=FALSE, crit.pca.distances=crit)
pc <- PcaHubert(A, alpha=alpha, k=ncol(A), mcd=if(ncol(A) == 1) TRUE else FALSE, crit.pca.distances=crit)
SD <- pc@sd
cutoff.sd <- pc@cutoff.sd
## A.cov <- CovMcd(A)
## SD <- sqrt(mahalanobis(A, center=getCenter(A.cov), cov=getCov(A.cov)))
## cutoff.sd <- sqrt(qchisq(crit, ncol(A)))
}else
{
A.cov <- CovClassic(A)
SD <- sqrt(mahalanobis(A, center=getCenter(A.cov), cov=getCov(A.cov)))
cutoff.sd <- sqrt(qchisq(crit, ncol(A)))
}
list(sd=SD, cutoff.sd=cutoff.sd)
}
## Classical PARAFAC
##
## - const: constraints (defaultes to "none"), orth=orthogonality constraints,
## nonneg=nonnegativity, zerocor=zero correlation constraints
.Parafac <- function (X, ncomp,
center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000, crit=0.975,
optim=c("als", "atld", "int2"),
trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
X <- do3Scale(X, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
Xwide <- unfold(X)
ret <- if(optim == "als") cp_als(X, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "atld") cp_atld(X, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(X, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
A <- ret$A
B <- ret$B
C <- ret$C
## Compute RD and SD with their cutoff values
Xfit <- A %*% t(krp(C, B))
rdsq <- apply((Xwide - Xfit)^2, 1, sum) # RD_i = ||X_i-Xhat_i||F; fit = sum(RD_i^2)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, robust=FALSE)
sd <- .cutoff.sd(A, crit=crit, robust=FALSE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## dimnames back
nfac <- paste0("F",1:ncomp)
dimnames(A) <- list(dn[[1]],nfac)
dimnames(B) <- list(dn[[2]],nfac)
dimnames(C) <- list(dn[[3]],nfac)
dimnames(Xfit) <- dn
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
ret <- list(fit=ret$fit, fp=ret$fp, ss=ret$ss, A=A, B=B, C=C, iter=ret$iter, const=ret$const,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
robust=FALSE, coda.transform="none")
class(ret) <- "parafac"
ret
}
## Robust PARAFAC
.Parafac.rob <- function (X, ncomp, center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "int2"),
ncomp.rpca, alpha=0.75, robiter=100, crit=0.975, trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
## If centering and/or scaling were requested, but no (robust) function
## was specified, take by default median and mad
if(is.logical(center) && center)
center <- median
if(is.logical(scale) && scale)
scale <- mad
X <- do3Scale(X, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
ssx <- sum(X^2)
Xwide <- unfold(X)
Ahat <- matrix(0, I, ncomp)
## define number of outliers the algorithm should resists
h <- round(alpha*I)
## Step 1 RobPCA of XA
if(trace)
cat("\nStep 1. Perform robust PCA on the unfolded matrix.")
outrobpca <- PcaHubert(Xwide, k=ncomp.rpca, kmax=ncol(Xwide), alpha=alpha, mcd=FALSE, trace=trace)
Hset <- sort(sort(outrobpca@od, index.return=TRUE)$ix[1:h])
Xhat <- Xwide[Hset,]
fitprev <- 0
changeFit <- 1 + conv
xiter <- iter <- 0
while (changeFit > conv & iter <= robiter)
{
iter <- iter + 1
## Step 2 - PARAFAC analysis
## ret <- cp_als(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xhat, h, J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
xiter <- xiter + ret$iter
Ah <- ret$A
Bh <- ret$B
Ch <- ret$C
## Step 3 - Fit the model
KR <- krp(Ch, Bh) # Khatri-Rao product
for(i in 1:I) {
vJKx1 <- matrix(X[i,,], 1, J*K)
Ahat[i,] <- pracma::pinv(KR) %*% t(vJKx1)
}
## The above is equivallent to the following:
## Ahat <- Xwide %*% t(pracma::pinv(KR))
Xfit <- Ahat %*% t(KR)
## Step 4 - Computation of the residual distances
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
Hset <- sort(sort(rdsq, index.return=TRUE)$ix[1:h])
fit <- sum(rdsq[Hset])
Xhat <- Xwide[Hset,]
## Step 5 Fit of the model
changeFit <- if(fitprev == 0) 1 + conv else abs(fit-fitprev)/fitprev
if(trace)
cat("\n---", toupper(optim), iter, "Fit, Fitprev, changeFit, iter", fit, fitprev, changeFit, ret$iter)
fitprev <- fit
}
if(trace)
cat("\n--- ---\n")
## Reweighting
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
flag <- rd <= cutoff.rd
Xflag <- X[flag,,]
Xflag_wide <- unfold(Xflag)
## ret <- cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
xiter <- xiter + ret$iter
Arew <- ret$A
Brew <- ret$B
Crew <- ret$C
KRrew <- krp(Crew, Brew) # Khatri-Rao product
Arew <- matrix(0, I, ncomp)
for(i in 1:I) {
vJKx1 <- matrix(X[i,,], 1, J*K)
Arew[i,] <- pracma::pinv(KRrew) %*% t(vJKx1)
}
## The above is equivallent to the following:
## Arew <- Xwide %*% t(pracma::pinv(KRrew))
Xfit <- Arew %*%t (KRrew)
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
fit <- sum(rdsq[rd <= cutoff.rd])
fp <- 100*(1-fit/ssx)
for(i in 1:ncomp) {
Arew[,i] <- Arew[,i]*norm(as.matrix(Brew[,i]),type="F")*norm(as.matrix(Crew[,i]),type="F")
Brew[,i] <- Brew[,i]/norm(as.matrix(Brew[,i]),type="F")
Crew[,i] <- Crew[,i]/norm(as.matrix(Crew[,i]),type="F")
}
sd <- .cutoff.sd(Arew, alpha=alpha, crit=crit, robust=TRUE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## dimnames back
nfac <- paste0("F", 1:ncomp)
dimnames(Arew) <- list(dn[[1]], nfac)
dimnames(Brew) <- list(dn[[2]], nfac)
dimnames(Crew) <- list(dn[[3]], nfac)
dimnames(Xfit) <- dn
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
res <- list(fit=fit, fp=fp, ss=ssx, A=Arew, B=Brew, C=Crew, iter=xiter, const=ret$const,
flag=flag, Hset=Hset, alpha=alpha,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
pcaobj=outrobpca, robiter=iter, robust=TRUE, coda.transform="none")
class(res) <- "parafac"
res
}
## Classical PARAFAC for compositional data
.Parafac.ilr <- function (X, ncomp, center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "atld", "int2"),
coda.transform=c("ilr", "clr"),
crit=0.975, trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
coda.transform <- match.arg(coda.transform)
## ncomp is the number of components
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
Xilr <- if(coda.transform == "ilr") ilrArray(X)
else if(coda.transform == "clr") clrArray(X)
else NULL
if(coda.transform == "ilr")
J <- J - 1
## centering the compositions
Xilr <- do3Scale(Xilr, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
Xwide <- unfold(Xilr)
ret <- if(optim == "als") cp_als(Xwide, I, J, K, ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "atld") cp_atld(Xwide, I, J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xwide, I, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
A <- ret$A
B <- ret$B
C <- ret$C
## Compute RD and SD with their cutoff values
Xfit <- A %*% t(krp(C, B))
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
fit <- sum(rdsq)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, robust=FALSE)
sd <- .cutoff.sd(A, crit=crit, robust=FALSE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## Back-transformation of loadings to clr
if(coda.transform == "clr") #do nothing
Bclr <- B
else
{
V <- matrix(0, nrow = J+1, ncol = J)
for(i in seq_len(ncol(V)))
{
V[1:i, i] <- 1/i
V[i + 1, i] <- (-1)
V[, i] <- V[, i] * sqrt(i/(i + 1))
}
Bclr <- V %*% B
}
## dimnames back
znames <- paste0("Z", 1:dim(B)[1])
nfac <- paste0("F", 1:ncomp)
dimnames(A) <- list(dn[[1]], nfac)
dimnames(B) <- if(coda.transform == "clr") list(dn[[2]], nfac) else list(znames, nfac)
dimnames(Bclr) <- list(dn[[2]], nfac)
dimnames(C) <- list(dn[[3]], nfac)
dimnames(Xfit) <- list(dn[[1]], znames, dn[[3]])
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
res <- list(fit=ret$fit, fp=ret$fp, ss=ret$ss, A=A, B=B, Bclr=Bclr, C=C, iter=ret$iter, const=ret$const,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
robust=FALSE, coda.transform=coda.transform)
class(res) <- "parafac"
res
}
## Robust PARAFAC for compositional data
.Parafac.rob.ilr <- function (X, ncomp, center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "int2"),
coda.transform=c("ilr"),
ncomp.rpca, alpha=0.75, robiter=100, crit=0.975, trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
coda.transform <- match.arg(coda.transform)
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
Xilr <- ilrArray(X)
J <- J - 1
## If centering and/or scaling were requested, but no (robust) function
## was specified, take by default median and mad
if(is.logical(center) && center)
center <- median
if(is.logical(scale) && scale)
scale <- mad
## centering the compositions
Xilr <- do3Scale(Xilr, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
ssx <- sum(Xilr^2)
Xwide <- unfold(Xilr)
Ahat <- matrix(0,dim(X)[1],ncomp)
## define number of outliers the algorithm should resists
h <- round(alpha * dim(X)[1])
## Step 1 RobPCA XA
outrobpca <- PcaHubert(Xwide, k=ncomp.rpca, kmax=ncol(Xwide), alpha=alpha, mcd=FALSE)
Hset <- sort(sort(outrobpca@od, index.return=TRUE)$ix[1:h])
Xhat <-Xwide[Hset,]
fitprev <- 0
changeFit <- 1 + conv
iter <- 0
while (changeFit > conv & iter <= robiter) {
iter <- iter+1
## Step 2 - PARAFAC analysis
## ret <- cp_als(Xhat, h, J, K, ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xhat, h, J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
Ah <- ret$A
Bh <- ret$B
Ch <- ret$C
KR <- krp(Ch, Bh) # Khatri-Rao product
for(i in 1:dim(X)[1]) {
vJKx1 <- matrix(Xilr[i, ,], 1, J*K)
Ahat[i,] <- pracma::pinv(KR) %*% t(vJKx1)
}
Xfit <- Ahat %*%t (KR)
## Step 4 Computation of the rd
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
Hset <- sort(sort(rdsq, index.return=TRUE)$ix[1:h])
fit <- sum(rdsq[Hset])
Xhat <- Xwide[Hset,]
## Step 5 Fit of the model
changeFit <- if(fitprev == 0) 1 + conv else abs(fit-fitprev)/fitprev
fitprev <- fit
}
## Reweighting
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
flag <- rd <= cutoff.rd
Xflag <- Xilr[flag,,]
Xflag_wide <- unfold(Xflag)
## ret <- cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
Arew <- ret$A
Brew <- ret$B
Crew <- ret$C
KR <- krp(Crew, Brew) # Khatri-Rao product
Arew <- matrix(0, I, ncomp)
for(i in 1:I) {
vJKx1 <- matrix(Xilr[i, ,], 1, J*K)
Arew[i,] <- pracma::pinv(KR) %*%t (vJKx1)
}
Xfit <- Arew %*% t(KR)
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
fit <- sum(rdsq[rd <= cutoff.rd])
fp <- 100*(1-fit/ssx)
for(i in 1:ncomp) {
Arew[,i] <- Arew[,i] * norm(as.matrix(Brew[,i]), type="F") * norm(as.matrix(Crew[,i]), type="F")
Brew[,i] <- Brew[,i] / norm(as.matrix(Brew[,i]), type="F")
Crew[,i] <- Crew[,i] / norm(as.matrix(Crew[,i]), type="F")
}
## Back-transformation of loadings to clr
V <- matrix(0, nrow = J+1, ncol = J)
for (i in seq_len(ncol(V))) {
V[1:i, i] <- 1/i
V[i + 1, i] <- (-1)
V[, i] <- V[, i] * sqrt(i/(i + 1))
}
Bclr <- V %*% Brew
sd <- .cutoff.sd(Arew, alpha=alpha, crit=crit, robust=TRUE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## dimnames back
nfac <- paste0("F", 1:ncomp)
znames <- paste0("Z", 1:dim(Brew)[1])
dimnames(Arew) <- list(dn[[1]], nfac)
dimnames(Brew) <- list(znames, nfac)
dimnames(Bclr) <- list(dn[[2]], nfac)
dimnames(Crew) <- list(dn[[3]], nfac)
dimnames(Xfit) <- list(dn[[1]], znames, dn[[3]])
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
res <- list(fit=fit, fp=fp, ss=ssx, A=Arew, B=Brew, Bclr=Bclr, C=Crew, iter=iter, const=ret$const,
flag=flag, Hset=Hset, alpha=alpha,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
pcaobj=outrobpca, robust=TRUE, coda.transform=coda.transform)
class(res) <- "parafac"
res
}
## - dd = distance-distance plot
## - comp = paired component plot for a single mode
## - percomp= per component plot
## - allcomp= all components plot
##
plot.parafac <- function(x, which=c("dd", "comp", "percomp", "allcomp", "all"), ask = (which=="all" && dev.interactive(TRUE)), id.n, ...)
{
which <- match.arg(which)
op <- if(ask) par(ask = TRUE) else list()
on.exit(par(op))
if((which == "all" || which == "dd")) {
ret <- .ddplot(x, id.n=id.n, ...) # distance-distance plot
}
if((which == "all" || which == "comp")) {
ret <- .compplot.parafac(x, ...) # paired components plot
}
if((which == "all" || which == "percomp")) {
ret <- .percompplot.parafac(x, ...) # per-component plot
}
if((which == "all" || which == "allcomp")) {
ret <- .allcompplot(x, ...) # all-component plot
}
invisible(ret)
}
print.parafac <- function(x, ...)
{
if(!is.null(cl <- x$call)) {
cat("Call:\n")
dput(cl)
cat("\n")
}
ncomp <- dim(x$A)[2]
cat("\nPARAFAC analysis with ", ncomp, " components.\nFit value:", x$fit,
"\nFit percentage:", round(x$fp,2), "%\n")
msg <- ""
if(x$robust) {
msg <- paste0(msg, "Robust")
if(x$coda.transform == "none")
msg <- paste0(msg, "\n")
}
if(x$coda.transform != "none"){
if(nchar(msg) > 0)
msg <- paste0(msg, ", ")
tr <- if(x$coda.transform == "clr") "clr-transformed" else "ilr-transformed"
msg <- paste0(msg, tr, "\n")
}
if(!is.null(x$optim) && x$optim != "als") {
msg <- paste0(msg, "Optimized with ", toupper(x$optim), ".\n")
}
cat(msg, "\n")
invisible(x)
}
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Defines functions print.parafac plot.parafac .cutoff.sd .cutoff.rd Parafac
Documented in Parafac plot.parafac print.parafac
Parafac <- function(X, ncomp=2,
center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "atld", "int2"),
robust=FALSE, coda.transform=c("none", "ilr", "clr"),
ncomp.rpca=0, alpha=0.75, robiter=100, crit=0.975, # arguments for the robust parafac
trace=FALSE)
{
call <- match.call()
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
if(optim == "atld" && robust)
stop("The robust option is not possible with 'atld' optimization. Please use 'als' or 'int2'.")
coda.transform <- match.arg(coda.transform)
ilr <- coda.transform != "none"
if(coda.transform == "clr" & robust)
stop("The robust option is not possible with 'clr' transform compositional data. Please use 'ilr'.")
if(length(crit) != 1 || crit <= 0 || crit >= 1)
stop("'crit' has to be a single positive number less than 1!")
if(crit < 0.5)
crit <- 1 - crit
stopifnot(alpha <= 1 & alpha >= 0.5)
ret <- if(robust & ilr) .Parafac.rob.ilr(X=X, ncomp=ncomp, # robust, compositional
center=center, center.mode=center.mode,
scale=scale, scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit,
coda.transform=coda.transform,
ncomp.rpca=ncomp.rpca, alpha=alpha, robiter=robiter,
trace=trace)
else if(!robust & !ilr) .Parafac(X=X, ncomp=ncomp, #
center=center, center.mode=center.mode, scale=scale,
scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit, optim=optim, trace=trace)
else if(!robust & ilr) .Parafac.ilr(X=X, ncomp=ncomp, # compositional
center=center, center.mode=center.mode,
scale=scale, scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit,
coda.transform=coda.transform,
trace=trace)
else if(robust & !ilr) .Parafac.rob(X=X, ncomp=ncomp, # robust
center=center, center.mode=center.mode,
scale=scale, scale.mode=scale.mode, const=const, conv=conv,
start=start, maxit=maxit, crit=crit, optim=optim,
ncomp.rpca=ncomp.rpca, alpha=alpha, robiter=robiter,
trace=trace)
## Total sum of squares, PARAFAC fit and fit percentage:
## ret$ss <- sum(X^2)
## ret$fit will be ||X_A - A G_A kron(C',B')||^2 where X_A and G_A denote the matricized (frontal slices) data array and core array
## ret$fp is equal to: 100*(ss-ret$fit)/ss
## Calculate the superdiagonal core g_sss and store it in GA
ret$GA <- sqrt(colSums(ret$A^2)) * sqrt(colSums(ret$B^2)) * sqrt(colSums(ret$C^2))
names(ret$GA) <- colnames(ret$A)
ret$ncomp <- ncomp
ret$optim <- optim
ret$call <- call
ret
}
.cutoff.rd <- function(rd, h, crit=0.975, robust=TRUE)
{
if(robust)
{
## a) Using median and MAD
## ret <- (median(rd^(2/3)) + mad(rd^(2/3)) * qnorm(crit))^(3/2)
##
## b) Using MASS cov.mcd (will need to import - library(MASS))
## unimcd <- cov.mcd(rd^(2/3),quantile.used=h)
## ret <- sqrt(qnorm(0.975, unimcd$center, sqrt(unimcd$cov))^3)
##
## c) Using UNIMCD
unimcd <- rrcov:::unimcd(rd^(2/3), quan=h)
ret <- sqrt(qnorm(crit, unimcd$tmcd, unimcd$smcd)^3)
## d) Using UNIMCD by CovMcd
## unimcd <- CovMcd(rd, alpha=h/length(rd))
## ret <- sqrt(qnorm(crit, getCenter(unimcd), sqrt(getCov(unimcd)))^3)
##
} else
ret <- (mean(rd^(2/3)) + sd(rd^(2/3)) * qnorm(crit))^(3/2)
ret
}
.cutoff.sd <- function(A, alpha, crit, robust=TRUE)
{
if(robust)
{
## VT::24.04.2020 Workaround - PcaHubert with mcd=FALSE will crash if A is one-dimensional matrix.
## now this is fixed in rrcov
##
## pc <- PcaHubert(A, alpha=alpha, k=ncol(A), mcd=FALSE, crit.pca.distances=crit)
pc <- PcaHubert(A, alpha=alpha, k=ncol(A), mcd=if(ncol(A) == 1) TRUE else FALSE, crit.pca.distances=crit)
SD <- pc@sd
cutoff.sd <- pc@cutoff.sd
## A.cov <- CovMcd(A)
## SD <- sqrt(mahalanobis(A, center=getCenter(A.cov), cov=getCov(A.cov)))
## cutoff.sd <- sqrt(qchisq(crit, ncol(A)))
}else
{
A.cov <- CovClassic(A)
SD <- sqrt(mahalanobis(A, center=getCenter(A.cov), cov=getCov(A.cov)))
cutoff.sd <- sqrt(qchisq(crit, ncol(A)))
}
list(sd=SD, cutoff.sd=cutoff.sd)
}
## Classical PARAFAC
##
## - const: constraints (defaultes to "none"), orth=orthogonality constraints,
## nonneg=nonnegativity, zerocor=zero correlation constraints
.Parafac <- function (X, ncomp,
center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000, crit=0.975,
optim=c("als", "atld", "int2"),
trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
X <- do3Scale(X, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
Xwide <- unfold(X)
ret <- if(optim == "als") cp_als(X, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "atld") cp_atld(X, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(X, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
A <- ret$A
B <- ret$B
C <- ret$C
## Compute RD and SD with their cutoff values
Xfit <- A %*% t(krp(C, B))
rdsq <- apply((Xwide - Xfit)^2, 1, sum) # RD_i = ||X_i-Xhat_i||F; fit = sum(RD_i^2)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, robust=FALSE)
sd <- .cutoff.sd(A, crit=crit, robust=FALSE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## dimnames back
nfac <- paste0("F",1:ncomp)
dimnames(A) <- list(dn[[1]],nfac)
dimnames(B) <- list(dn[[2]],nfac)
dimnames(C) <- list(dn[[3]],nfac)
dimnames(Xfit) <- dn
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
ret <- list(fit=ret$fit, fp=ret$fp, ss=ret$ss, A=A, B=B, C=C, iter=ret$iter, const=ret$const,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
robust=FALSE, coda.transform="none")
class(ret) <- "parafac"
ret
}
## Robust PARAFAC
.Parafac.rob <- function (X, ncomp, center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "int2"),
ncomp.rpca, alpha=0.75, robiter=100, crit=0.975, trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
## If centering and/or scaling were requested, but no (robust) function
## was specified, take by default median and mad
if(is.logical(center) && center)
center <- median
if(is.logical(scale) && scale)
scale <- mad
X <- do3Scale(X, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
ssx <- sum(X^2)
Xwide <- unfold(X)
Ahat <- matrix(0, I, ncomp)
## define number of outliers the algorithm should resists
h <- round(alpha*I)
## Step 1 RobPCA of XA
if(trace)
cat("\nStep 1. Perform robust PCA on the unfolded matrix.")
outrobpca <- PcaHubert(Xwide, k=ncomp.rpca, kmax=ncol(Xwide), alpha=alpha, mcd=FALSE, trace=trace)
Hset <- sort(sort(outrobpca@od, index.return=TRUE)$ix[1:h])
Xhat <- Xwide[Hset,]
fitprev <- 0
changeFit <- 1 + conv
xiter <- iter <- 0
while (changeFit > conv & iter <= robiter)
{
iter <- iter + 1
## Step 2 - PARAFAC analysis
## ret <- cp_als(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xhat, h, J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
xiter <- xiter + ret$iter
Ah <- ret$A
Bh <- ret$B
Ch <- ret$C
## Step 3 - Fit the model
KR <- krp(Ch, Bh) # Khatri-Rao product
for(i in 1:I) {
vJKx1 <- matrix(X[i,,], 1, J*K)
Ahat[i,] <- pracma::pinv(KR) %*% t(vJKx1)
}
## The above is equivallent to the following:
## Ahat <- Xwide %*% t(pracma::pinv(KR))
Xfit <- Ahat %*% t(KR)
## Step 4 - Computation of the residual distances
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
Hset <- sort(sort(rdsq, index.return=TRUE)$ix[1:h])
fit <- sum(rdsq[Hset])
Xhat <- Xwide[Hset,]
## Step 5 Fit of the model
changeFit <- if(fitprev == 0) 1 + conv else abs(fit-fitprev)/fitprev
if(trace)
cat("\n---", toupper(optim), iter, "Fit, Fitprev, changeFit, iter", fit, fitprev, changeFit, ret$iter)
fitprev <- fit
}
if(trace)
cat("\n--- ---\n")
## Reweighting
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
flag <- rd <= cutoff.rd
Xflag <- X[flag,,]
Xflag_wide <- unfold(Xflag)
## ret <- cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
xiter <- xiter + ret$iter
Arew <- ret$A
Brew <- ret$B
Crew <- ret$C
KRrew <- krp(Crew, Brew) # Khatri-Rao product
Arew <- matrix(0, I, ncomp)
for(i in 1:I) {
vJKx1 <- matrix(X[i,,], 1, J*K)
Arew[i,] <- pracma::pinv(KRrew) %*% t(vJKx1)
}
## The above is equivallent to the following:
## Arew <- Xwide %*% t(pracma::pinv(KRrew))
Xfit <- Arew %*%t (KRrew)
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
fit <- sum(rdsq[rd <= cutoff.rd])
fp <- 100*(1-fit/ssx)
for(i in 1:ncomp) {
Arew[,i] <- Arew[,i]*norm(as.matrix(Brew[,i]),type="F")*norm(as.matrix(Crew[,i]),type="F")
Brew[,i] <- Brew[,i]/norm(as.matrix(Brew[,i]),type="F")
Crew[,i] <- Crew[,i]/norm(as.matrix(Crew[,i]),type="F")
}
sd <- .cutoff.sd(Arew, alpha=alpha, crit=crit, robust=TRUE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## dimnames back
nfac <- paste0("F", 1:ncomp)
dimnames(Arew) <- list(dn[[1]], nfac)
dimnames(Brew) <- list(dn[[2]], nfac)
dimnames(Crew) <- list(dn[[3]], nfac)
dimnames(Xfit) <- dn
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
res <- list(fit=fit, fp=fp, ss=ssx, A=Arew, B=Brew, C=Crew, iter=xiter, const=ret$const,
flag=flag, Hset=Hset, alpha=alpha,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
pcaobj=outrobpca, robiter=iter, robust=TRUE, coda.transform="none")
class(res) <- "parafac"
res
}
## Classical PARAFAC for compositional data
.Parafac.ilr <- function (X, ncomp, center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "atld", "int2"),
coda.transform=c("ilr", "clr"),
crit=0.975, trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
coda.transform <- match.arg(coda.transform)
## ncomp is the number of components
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
Xilr <- if(coda.transform == "ilr") ilrArray(X)
else if(coda.transform == "clr") clrArray(X)
else NULL
if(coda.transform == "ilr")
J <- J - 1
## centering the compositions
Xilr <- do3Scale(Xilr, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
Xwide <- unfold(Xilr)
ret <- if(optim == "als") cp_als(Xwide, I, J, K, ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "atld") cp_atld(Xwide, I, J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xwide, I, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
A <- ret$A
B <- ret$B
C <- ret$C
## Compute RD and SD with their cutoff values
Xfit <- A %*% t(krp(C, B))
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
fit <- sum(rdsq)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, robust=FALSE)
sd <- .cutoff.sd(A, crit=crit, robust=FALSE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## Back-transformation of loadings to clr
if(coda.transform == "clr") #do nothing
Bclr <- B
else
{
V <- matrix(0, nrow = J+1, ncol = J)
for(i in seq_len(ncol(V)))
{
V[1:i, i] <- 1/i
V[i + 1, i] <- (-1)
V[, i] <- V[, i] * sqrt(i/(i + 1))
}
Bclr <- V %*% B
}
## dimnames back
znames <- paste0("Z", 1:dim(B)[1])
nfac <- paste0("F", 1:ncomp)
dimnames(A) <- list(dn[[1]], nfac)
dimnames(B) <- if(coda.transform == "clr") list(dn[[2]], nfac) else list(znames, nfac)
dimnames(Bclr) <- list(dn[[2]], nfac)
dimnames(C) <- list(dn[[3]], nfac)
dimnames(Xfit) <- list(dn[[1]], znames, dn[[3]])
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
res <- list(fit=ret$fit, fp=ret$fp, ss=ret$ss, A=A, B=B, Bclr=Bclr, C=C, iter=ret$iter, const=ret$const,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
robust=FALSE, coda.transform=coda.transform)
class(res) <- "parafac"
res
}
## Robust PARAFAC for compositional data
.Parafac.rob.ilr <- function (X, ncomp, center=FALSE, center.mode=c("A", "B", "C", "AB", "AC", "BC", "ABC"),
scale=FALSE, scale.mode=c("B", "A", "C"),
const="none", conv=1e-6, start="svd", maxit=10000,
optim=c("als", "int2"),
coda.transform=c("ilr"),
ncomp.rpca, alpha=0.75, robiter=100, crit=0.975, trace=FALSE)
{
center.mode <- match.arg(center.mode)
scale.mode <- match.arg(scale.mode)
optim <- match.arg(optim)
coda.transform <- match.arg(coda.transform)
di <- dim(X)
I <- di[1]
J <- di[2]
K <- di[3]
dn <- dimnames(X)
Xilr <- ilrArray(X)
J <- J - 1
## If centering and/or scaling were requested, but no (robust) function
## was specified, take by default median and mad
if(is.logical(center) && center)
center <- median
if(is.logical(scale) && scale)
scale <- mad
## centering the compositions
Xilr <- do3Scale(Xilr, center=center, center.mode=center.mode, scale=scale, scale.mode=scale.mode)
ssx <- sum(Xilr^2)
Xwide <- unfold(Xilr)
Ahat <- matrix(0,dim(X)[1],ncomp)
## define number of outliers the algorithm should resists
h <- round(alpha * dim(X)[1])
## Step 1 RobPCA XA
outrobpca <- PcaHubert(Xwide, k=ncomp.rpca, kmax=ncol(Xwide), alpha=alpha, mcd=FALSE)
Hset <- sort(sort(outrobpca@od, index.return=TRUE)$ix[1:h])
Xhat <-Xwide[Hset,]
fitprev <- 0
changeFit <- 1 + conv
iter <- 0
while (changeFit > conv & iter <= robiter) {
iter <- iter+1
## Step 2 - PARAFAC analysis
## ret <- cp_als(Xhat, h, J, K, ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xhat, h, J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xhat, h, J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
Ah <- ret$A
Bh <- ret$B
Ch <- ret$C
KR <- krp(Ch, Bh) # Khatri-Rao product
for(i in 1:dim(X)[1]) {
vJKx1 <- matrix(Xilr[i, ,], 1, J*K)
Ahat[i,] <- pracma::pinv(KR) %*% t(vJKx1)
}
Xfit <- Ahat %*%t (KR)
## Step 4 Computation of the rd
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
Hset <- sort(sort(rdsq, index.return=TRUE)$ix[1:h])
fit <- sum(rdsq[Hset])
Xhat <- Xwide[Hset,]
## Step 5 Fit of the model
changeFit <- if(fitprev == 0) 1 + conv else abs(fit-fitprev)/fitprev
fitprev <- fit
}
## Reweighting
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
flag <- rd <= cutoff.rd
Xflag <- Xilr[flag,,]
Xflag_wide <- unfold(Xflag)
## ret <- cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
ret <- if(optim == "als") cp_als(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
## else if(optim == "atld") cp_atld(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, conv=conv, start=start, maxit=maxit, trace=trace)
else if(optim == "int2") cp_int2(Xflag_wide, nrow(Xflag_wide), J, K, ncomp=ncomp, const=const, conv=conv, start=start, maxit=maxit, trace=trace)
else
stop(paste("Unknown optimization method:", optim, "!"))
Arew <- ret$A
Brew <- ret$B
Crew <- ret$C
KR <- krp(Crew, Brew) # Khatri-Rao product
Arew <- matrix(0, I, ncomp)
for(i in 1:I) {
vJKx1 <- matrix(Xilr[i, ,], 1, J*K)
Arew[i,] <- pracma::pinv(KR) %*%t (vJKx1)
}
Xfit <- Arew %*% t(KR)
rdsq <- apply((Xwide - Xfit)^2, 1, sum)
rd <- sqrt(rdsq)
cutoff.rd <- .cutoff.rd(rd, crit=crit, h)
fit <- sum(rdsq[rd <= cutoff.rd])
fp <- 100*(1-fit/ssx)
for(i in 1:ncomp) {
Arew[,i] <- Arew[,i] * norm(as.matrix(Brew[,i]), type="F") * norm(as.matrix(Crew[,i]), type="F")
Brew[,i] <- Brew[,i] / norm(as.matrix(Brew[,i]), type="F")
Crew[,i] <- Crew[,i] / norm(as.matrix(Crew[,i]), type="F")
}
## Back-transformation of loadings to clr
V <- matrix(0, nrow = J+1, ncol = J)
for (i in seq_len(ncol(V))) {
V[1:i, i] <- 1/i
V[i + 1, i] <- (-1)
V[, i] <- V[, i] * sqrt(i/(i + 1))
}
Bclr <- V %*% Brew
sd <- .cutoff.sd(Arew, alpha=alpha, crit=crit, robust=TRUE)
flag <- rd <= cutoff.rd & sd$sd <= sd$cutoff.sd
Xfit <- toArray(Xfit, I, J, K)
## dimnames back
nfac <- paste0("F", 1:ncomp)
znames <- paste0("Z", 1:dim(Brew)[1])
dimnames(Arew) <- list(dn[[1]], nfac)
dimnames(Brew) <- list(znames, nfac)
dimnames(Bclr) <- list(dn[[2]], nfac)
dimnames(Crew) <- list(dn[[3]], nfac)
dimnames(Xfit) <- list(dn[[1]], znames, dn[[3]])
names(rd) <- names(sd$sd) <- names(flag) <- dn[[1]]
res <- list(fit=fit, fp=fp, ss=ssx, A=Arew, B=Brew, Bclr=Bclr, C=Crew, iter=iter, const=ret$const,
flag=flag, Hset=Hset, alpha=alpha,
Xhat=Xfit, rd=rd, cutoff.rd=cutoff.rd, sd=sd$sd, cutoff.sd=sd$cutoff.sd,
pcaobj=outrobpca, robust=TRUE, coda.transform=coda.transform)
class(res) <- "parafac"
res
}
## - dd = distance-distance plot
## - comp = paired component plot for a single mode
## - percomp= per component plot
## - allcomp= all components plot
##
plot.parafac <- function(x, which=c("dd", "comp", "percomp", "allcomp", "all"), ask = (which=="all" && dev.interactive(TRUE)), id.n, ...)
{
which <- match.arg(which)
op <- if(ask) par(ask = TRUE) else list()
on.exit(par(op))
if((which == "all" || which == "dd")) {
ret <- .ddplot(x, id.n=id.n, ...) # distance-distance plot
}
if((which == "all" || which == "comp")) {
ret <- .compplot.parafac(x, ...) # paired components plot
}
if((which == "all" || which == "percomp")) {
ret <- .percompplot.parafac(x, ...) # per-component plot
}
if((which == "all" || which == "allcomp")) {
ret <- .allcompplot(x, ...) # all-component plot
}
invisible(ret)
}
print.parafac <- function(x, ...)
{
if(!is.null(cl <- x$call)) {
cat("Call:\n")
dput(cl)
cat("\n")
}
ncomp <- dim(x$A)[2]
cat("\nPARAFAC analysis with ", ncomp, " components.\nFit value:", x$fit,
"\nFit percentage:", round(x$fp,2), "%\n")
msg <- ""
if(x$robust) {
msg <- paste0(msg, "Robust")
if(x$coda.transform == "none")
msg <- paste0(msg, "\n")
}
if(x$coda.transform != "none"){
if(nchar(msg) > 0)
msg <- paste0(msg, ", ")
tr <- if(x$coda.transform == "clr") "clr-transformed" else "ilr-transformed"
msg <- paste0(msg, tr, "\n")
}
if(!is.null(x$optim) && x$optim != "als") {
msg <- paste0(msg, "Optimized with ", toupper(x$optim), ".\n")
}
cat(msg, "\n")
invisible(x)
}
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