Nothing
NTD <- function(X, M=NULL, pseudocount=.Machine$double.eps,
initS=NULL, initA=NULL, fixS=FALSE, fixA=FALSE,
L1_A=1e-10, L2_A=1e-10, rank = rep(3, length=length(dim(X))),
modes = seq_along(dim(X)),
algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "HALS", "Alpha", "Beta", "NMF"),
init = c("NMF", "ALS", "Random"),
nmf.algorithm = c("Frobenius", "KL", "IS", "Pearson", "Hellinger", "Neyman", "Alpha", "Beta", "ALS", "PGD", "HALS", "GCD", "Projected", "NHR", "DTPP", "Orthogonal", "OrthReg"),
Alpha = 1, Beta = 2, thr = 1e-10, num.iter = 100,
num.iter2 = 10, viz = FALSE,
figdir = NULL, verbose = FALSE){
# Argument check
algorithm <- match.arg(algorithm)
init <- match.arg(init)
.checkNTD(X, M, pseudocount, rank, modes, initS, initA, fixS, fixA,
Alpha, Beta, thr, num.iter, viz, figdir, verbose)
# Initialization of An and S
int <- .initNTD(X, M, pseudocount, fixA, rank, modes, init, initS, initA,
Alpha, Beta, algorithm, thr, verbose)
X <- int$X
M <- int$M
pM <- int$pM
M_NA <- int$M_NA
fixA <- int$fixA
modes <- int$modes
N <- int$N
A <- int$A
S <- int$S
rank <- int$rank
RecError <- int$RecError
TrainRecError <- int$TrainRecError
TestRecError <- int$TestRecError
RelChange <- int$RelChange
Alpha <- int$Alpha
Beta <- int$Beta
algorithm <- int$algorithm
E <- int$E
J_hat <- int$J_hat
iter <- 1
while ((RecError[iter] > thr) && (iter <= num.iter)) {
X_bar <- recTensor(S=S, A=A, idx=modes)
pre_Error <- .recError(X, X_bar)
# Update An
for (n in modes) {
if(!fixA[n]){
if (algorithm == "Alpha") {
S_A <- t(cs_unfold(S, m = n)@data) %*% kronecker_list(sapply(rev(setdiff(1:N,
n)), function(x) {
A[[x]]
}, simplify = FALSE))
Xn <- cs_unfold(X, m = n)@data
pMn <- cs_unfold(pM, m = n)@data
numer <- S_A %*% (pMn * (Xn/t(t(A[[n]]) %*% S_A)))^Alpha
denom <- t(as.matrix(rep(1, dim(X)[n]) %*% t(rowSums(S_A))))
A[[n]] <- A[[n]] * (numer/denom)^(1/Alpha)
}else if (algorithm == "Beta") {
S_A <- t(cs_unfold(S, m = n)@data) %*% kronecker_list(sapply(rev(setdiff(1:N,
n)), function(x) {
A[[x]]
}, simplify = FALSE))
Xn <- cs_unfold(X, m = n)@data
pMn <- cs_unfold(pM, m = n)@data
Xn_bar <- cs_unfold(recTensor(S=S, A=A), m = n)@data
numer <- S_A %*% ((pMn * Xn) * (pMn * Xn_bar^(Beta - 1)))
denom <- S_A %*% (t(S_A) %*% A[[n]])^Beta
A[[n]] <- A[[n]] * (numer / (denom + L1_A + L2_A * A[[n]]))^.rho(Beta)
}else if (algorithm == "HALS") {
X_bar <- recTensor(S=S, A=A, idx = setdiff(1:N, n))
for (jn in 1:nrow(A[[n]])) {
X_barkn <- .slice(X_bar, mode = n, column = jn)
wjn <- fnorm(X_barkn)^2
ajn <- .positive(A[[n]][jn, ] + .contProd(E,
X_barkn, mode = n)/wjn)
E <- E + ttm(X_barkn, as.matrix(A[[n]][jn,
] - ajn), m = n)
A[[n]][jn, ] <- ajn / norm(as.matrix(ajn), "F")
}
}else if(algorithm == "NMF"){
Xn <- t(cs_unfold(X, m = n)@data)
pMn <- t(cs_unfold(pM, m = n)@data)
A[[n]] <- t(NMF(X=Xn, M=pMn,
initU=t(A[[n]]),
pseudocount=pseudocount, fixU=fixA[n],
L1_U=L1_A, L2_U=L2_A,
J=rank[n], algorithm=nmf.algorithm,
Alpha=Alpha, Beta=Beta,
num.iter=num.iter2, verbose=verbose)$U)
}else{
stop("Please specify the appropriate algorithm\n")
}
}
}
#
# Normalization of factor matrices
#
for (n in modes) {
A[[n]] <- t(apply(A[[n]], 1, function(x) {
x/norm(as.matrix(x), "F")
}))
}
#
# Update Core tensor
#
if(!fixS){
if (algorithm == "Alpha"){
S <- .positive(recTensor(S=X, A=A, idx=modes, reverse = TRUE))
numer <- pM * (X/recTensor(S=S, A=A, idx=modes))^Alpha
denom <- X
cmd <- paste0("denom[",
paste(rep("", length=length(dim(X))), collapse=","), "] <- 1")
eval(parse(text=cmd))
denom <- pM * denom
for (n in 1:N) {
numer <- ttm(numer, A[[n]], m = n)
denom <- ttm(denom, A[[n]], m = n)
}
S <- S * (numer/denom)^(1/Alpha)
}else if (algorithm %in% c("Beta", "NMF")){
X_bar <- recTensor(S=S, A=A, idx=modes)
numer <- pM * X * X_bar^(Beta - 1)
denom <- pM * X_bar^Beta
for (n in 1:N) {
numer <- ttm(numer, A[[n]], m = n)
denom <- ttm(denom, A[[n]], m = n)
}
S <- S * numer/denom
}else if (algorithm == "HALS"){
for (j_ijk in 1:length(J_hat)) {
eval(parse(text=.HALSCMD2(N)))
eval(parse(text=.HALSCMD3(N)))
eval(parse(text=.HALSCMD4(N)))
eval(parse(text=.HALSCMD5(N)))
eval(parse(text=.HALSCMD6(N)))
eval(parse(text=.HALSCMD7(N)))
}
}else{
stop("Please specify the appropriate algorithm\n")
}
}
# NaN
for (n in modes) {
if (any(is.infinite(A[[n]])) || any(is.nan(A[[n]]))) {
stop("Inf or NaN is generated!\n")
}
}
# After Update U, V
iter <- iter + 1
X_bar <- recTensor(S=S, A=A, idx=modes)
RecError[iter] <- .recError(X, X_bar)
TrainRecError[iter] <- .recError((1-M_NA+M)*X, (1-M_NA+M)*X_bar)
TestRecError[iter] <- .recError((M_NA-M)*X, (M_NA-M)*X_bar)
RelChange[iter] <- abs(pre_Error - RecError[iter]) / RecError[iter]
if (viz && !is.null(figdir) && N == 3) {
png(filename = paste0(figdir, "/", iter, ".png"))
plotTensor3D(X_bar)
dev.off()
}
if (viz && is.null(figdir) && N == 3) {
plotTensor3D(X_bar)
}
if (verbose) {
cat(paste0(iter-1, " / ", num.iter, " |Previous Error - Error| / Error = ",
RelChange[iter], "\n"))
}
if (is.nan(RelChange[iter])) {
stop("NaN is generated. Please run again or change the parameters.\n")
}
}
if (viz && !is.null(figdir) && N == 3) {
png(filename = paste0(figdir, "/finish.png"))
plotTensor3D(X_bar)
dev.off()
png(filename = paste0(figdir, "/original.png"))
plotTensor3D(X)
dev.off()
}
if (viz && is.null(figdir) && N == 3) {
plotTensor3D(X_bar)
}
names(RecError) <- c("offset", seq_len(iter-1))
names(TrainRecError) <- c("offset", seq_len(iter-1))
names(TestRecError) <- c("offset", seq_len(iter-1))
names(RelChange) <- c("offset", seq_len(iter-1))
return(list(S = S, A = A,
RecError = RecError,
TrainRecError = TrainRecError,
TestRecError = TestRecError,
RelChange = RelChange))
}
.checkNTD <- function(X, M, pseudocount, rank, modes, initS, initA, fixS, fixA,
Alpha, Beta, thr, num.iter, viz, figdir, verbose){
stopifnot(is.array(X@data))
if(!is.null(M)){
if(!identical(dim(X), dim(M))){
stop("Please specify the dimensions of X and M are same")
}
.checkZeroNA(X, M, type="Tensor")
}
stopifnot(is.numeric(pseudocount))
if(!is.null(initS)){
dimS <- as.numeric(dim(initS)[modes])
if(!identical(rank, dimS)){
stop("Please specify the rank and dim(S) are same")
}
}
if(!is.null(initA)){
nrowA <- as.numeric(unlist(lapply(initA, nrow)))[modes]
if(!identical(rank, nrowA)){
stop("Please specify the rank and nrow(A[[k]]) are same")
}
}
if(!is.logical(fixS)){
if(!"Tensor" %in% is(X)){
stop("Please specify the fixS as a logical or a Tensor object")
}else{
if(!identical(rank, dim(fixS))){
stop("Please specify the dimensions of fixS same as the rank")
}
}
}
if(!is.logical(fixA)){
if(!is.vector(fixA)){
stop("Please specify the fixA as a logical or a logical vector such as c(TRUE, FALSE, TRUE)")
}else{
if(length(modes) != length(fixA)){
stop("Please specify the length of fixA same as length(modes)")
}
}
}
stopifnot(is.numeric(rank))
stopifnot(is.numeric(modes))
stopifnot(is.numeric(Alpha))
stopifnot(is.numeric(Beta))
stopifnot(is.numeric(thr))
stopifnot(is.numeric(num.iter))
stopifnot(is.logical(viz))
stopifnot(is.logical(verbose))
if(!is.character(figdir) && !is.null(figdir)){
stop("Please specify the figdir as a string or NULL")
}
if (verbose) {
cat("Initialization step is running...\n")
}
}
.initNTD <- function(X, M, pseudocount, fixA, rank, modes, init, initS, initA,
Alpha, Beta, algorithm, thr, verbose){
N <- length(dim(X))
tmp <- rep(FALSE, length=length(dim(X)))
tmp[modes] <- fixA
fixA <- tmp
# modes
modes <- unique(modes)
modes <- modes[order(modes)]
if(length(modes) != length(rank)){
stop("Please the length(modes) and length(rank) as same")
}
# NA mask
M_NA <- X
M_NA@data[] <- 1
M_NA@data[which(is.na(X@data))] <- 0
if(is.null(M)){
M <- M_NA
}
pM <- M
# Pseudo count
X@data[which(is.na(X@data))] <- pseudocount
X <- .pseudocount(X, pseudocount)
pM <- .pseudocount(M, pseudocount)
A <- list()
length(A) <- N
Iposition <- setdiff(seq_len(N), modes)
rank <- .insertNULL(rank, Iposition, N)
if(is.null(initA)){
if (init == "NMF") {
sapply(modes, function(n) {
Xn <- cs_unfold(X, m = n)@data
An <- t(NMF(Xn, J = rank[n], algorithm = "KL")$V)
A[[n]] <<- t(apply(An, 1, function(x) {
x/norm(as.matrix(x), "F")
}))
})
} else if (init == "ALS") {
sapply(modes, function(n) {
Xn <- cs_unfold(X, m = n)@data
res.svd <- svd(Xn)
An <- t(.positive(res.svd$v[, seq(rank[n])]))
A[[n]] <<- t(apply(An, 1, function(x){
x/norm(as.matrix(x), "F")}))
})
} else if (init == "Random") {
sapply(modes, function(n) {
A[[n]] <<- matrix(runif(rank[n] * dim(X)[n]),
nrow = rank[n], ncol = dim(X)[n])
})
}
sapply(Iposition, function(n){
A[[n]] <<- diag(dim(X)[n])
})
}else{
A <- initA
}
names(A)[modes] <- paste0("A", modes)
names(A)[Iposition] <- paste0("I", seq_along(Iposition))
if(is.null(initS)){
S <- recTensor(S=X, A=A, idx=modes, reverse = TRUE)
}else{
S <- initS
}
RecError = c()
TrainRecError = c()
TestRecError = c()
RelChange = c()
RecError[1] <- thr * 10
TrainRecError[1] <- thr * 10
TestRecError[1] <- thr * 10
RelChange[1] <- thr * 10
E <- NULL
J_hat <- NULL
if (algorithm == "HALS") {
E <- X - recTensor(S=S, A=A, idx=modes)
eval(parse(text=.HALSCMD1(N)))
}
if (algorithm == "Frobenius") {
Beta = 2
algorithm = "Beta"
}
if (algorithm == "KL") {
Alpha = 1
algorithm = "Alpha"
}
if (algorithm == "IS") {
Beta = 0
algorithm = "Beta"
}
if (algorithm == "Pearson") {
Alpha = 2
algorithm = "Alpha"
}
if (algorithm == "Hellinger") {
Alpha = 0.5
algorithm = "Alpha"
}
if (algorithm == "Neyman") {
Alpha = -1
algorithm = "Alpha"
}
if(algorithm == "NMF"){
Beta = 2
}
if (verbose) {
cat("Iterative step is running...\n")
}
list(X=X, M=M, pM=pM, M_NA=M_NA, fixA=fixA, modes=modes, N=N,
A=A, S=S, rank=rank,
RecError=RecError, TrainRecError=TrainRecError,
TestRecError=TestRecError, RelChange=RelChange,
Alpha=Alpha, Beta=Beta,
algorithm=algorithm, E=E, J_hat=J_hat)
}
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