Nothing
R/parafac.R
In multiway: Component Models for Multi-Way Data
parafac <-
function(X, nfac, nstart = 10, const = NULL, control = NULL,
Afixed = NULL, Bfixed = NULL, Cfixed = NULL, Dfixed = NULL,
Astart = NULL, Bstart = NULL, Cstart = NULL, Dstart = NULL,
Astruc = NULL, Bstruc = NULL, Cstruc = NULL, Dstruc = NULL,
Amodes = NULL, Bmodes = NULL, Cmodes = NULL, Dmodes = NULL,
maxit = 500, ctol = 1e-4, parallel = FALSE, cl = NULL,
output = c("best", "all"), verbose = TRUE, backfit = FALSE){
# 3-way or 4-way Parallel Factor Analysis (Parafac)
# via alternating least squares (ALS) with optional constraints
# Nathaniel E. Helwig (helwig@umn.edu)
# last updated: May 25, 2018
# check 'X' input
xdim <- dim(X)
lxdim <- length(xdim)
if((lxdim < 3L) | (lxdim > 4L)) stop("Input 'X' must be 3-way or 4-way array")
if(any(is.nan(X)) | any(is.infinite(X))) stop("Input 'X' cannot contain NaN or Inf values")
if(any(is.na(X))){
missingdata <- TRUE
naid <- which(is.na(X))
} else {
missingdata <- FALSE
xcx <- sumsq(X)
}
# check 'nfac' and 'nstart' inputs
nfac <- as.integer(nfac[1])
if(nfac<1L){stop("Input 'nfac' must be positive integer")}
nstart <- as.integer(nstart[1])
if(nstart<1L){stop("Input 'nstart' must be positive integer")}
# check 'maxit' and 'ctol' inputs
maxit <- as.integer(maxit[1])
if(maxit<1L){stop("Input 'maxit' must be positive integer")}
ctol <- as.numeric(ctol[1])
if(ctol<0L){stop("Input 'ctol' must be positive numeric")}
# const types: old, new, and spline
const.oldtypes <- c("uncons", "orthog", "nonneg",
"unismo", "monsmo", "smoper", "smooth")
const.newtypes <- c("uncons", "nonneg", "period", "pernon",
"smooth", "smonon", "smoper", "smpeno",
"orthog", "ortnon", "ortsmo", "orsmpe",
"moninc", "monnon", "monsmo", "mosmno",
"unimod", "uninon", "uniper", "unpeno",
"unismo", "unsmno", "unsmpe", "unsmpn")
const.smooth <- c("smooth", "smonon", "smoper", "smpeno",
"ortsmo", "orsmpe", "monsmo", "mosmno",
"unismo", "unsmno", "unsmpe", "unsmpn")
const.unimod <- c("unimod", "uninon", "uniper", "unpeno",
"unismo", "unsmno", "unsmpe", "unsmpn")
# check 'const' input
if(is.null(const)){
const <- rep("uncons", lxdim)
} else {
if(length(const) != lxdim) stop("Input 'const' must be ",lxdim," element vector specifying constraint for each mode")
if(is.integer(const) | is.numeric(const)){
const <- as.integer(const)
if(any(is.na(const))) const[is.na(const)] <- 0L
if(any(const < 0L) | any(const > 6L)) stop("Input 'const' must contain characters (preferred) or integers between 0 and 6.")
const <- const.oldtypes[const + 1L]
} else {
const <- as.character(const)
if(any(is.na(const))) const[is.na(const)] <- "uncons"
cid <- pmatch(const, const.newtypes, duplicates.ok = TRUE)
if(any(is.na(cid))) stop("Input 'const' must be a character vector of length ",lxdim,"\n with each element matching one of the 24 available options.")
const <- const.newtypes[cid]
}
} # end if(is.null(const))
# check 'control' input
convars <- list(const=const, df=control$df, degree=control$degree, intercept=control$intercept)
control <- do.call("const.control", convars)
for(j in 1:length(const)){
if(any(const[j] == const.smooth)){
if(control$df[j] >= xdim[j]) {
warning(paste0("Input control$df[",j,"] = ",control$df[j]," >= dim(X)[",j,"] = ",xdim[j],"\nResetting control$df[",j,"] = ",xdim[j]-1,"."))
control$df[j] <- xdim[j] - 1
}
}
}
# check 'Afixed' and 'Bfixed' and 'Cfixed' inputs
if(!is.null(Afixed)){
Afixed <- as.matrix(Afixed)
if(nrow(Afixed)!=xdim[1]){stop("Input 'Afixed' must have the same number of rows as dim(X)[1]")}
if(ncol(Afixed)!=nfac){stop("Input 'Afixed' must have 'nfac' columns")}
}
if(!is.null(Bfixed)){
Bfixed <- as.matrix(Bfixed)
if(nrow(Bfixed)!=xdim[2]){stop("Input 'Bfixed' must have the same number of rows as dim(X)[2]")}
if(ncol(Bfixed)!=nfac){stop("Input 'Bfixed' must have 'nfac' columns")}
}
if(!is.null(Cfixed)){
Cfixed <- as.matrix(Cfixed)
if(nrow(Cfixed)!=xdim[3]){stop("Input 'Cfixed' must have the same number of rows as dim(X)[3]")}
if(ncol(Cfixed)!=nfac){stop("Input 'Cfixed' must have 'nfac' columns")}
}
# check 'Astart' and 'Bstart' and 'Cstart' inputs
if(!is.null(Astart)){
Astart <- as.matrix(Astart)
if(nrow(Astart)!=xdim[1]){stop("Input 'Astart' must have the same number of rows as dim(X)[1]")}
if(ncol(Astart)!=nfac){stop("Input 'Astart' must have 'nfac' columns")}
}
if(!is.null(Bstart)){
Bstart <- as.matrix(Bstart)
if(nrow(Bstart)!=xdim[2]){stop("Input 'Bstart' must have the same number of rows as dim(X)[2]")}
if(ncol(Bstart)!=nfac){stop("Input 'Bstart' must have 'nfac' columns")}
}
if(!is.null(Cstart)){
Cstart <- as.matrix(Cstart)
if(nrow(Cstart)!=xdim[3]){stop("Input 'Cstart' must have the same number of rows as dim(X)[3]")}
if(ncol(Cstart)!=nfac){stop("Input 'Cstart' must have 'nfac' columns")}
}
# check 'Astruc' and 'Bstruc' and 'Cstruc' inputs
if(!is.null(Astruc)){
Astruc <- as.matrix(Astruc)
if(nrow(Astruc)!=xdim[1]){stop("Input 'Astruc' must have the same number of rows as dim(X)[1]")}
if(ncol(Astruc)!=nfac){stop("Input 'Astruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Astruc,1:2,class)))){stop("Input 'Astruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
if(!is.null(Bstruc)){
Bstruc <- as.matrix(Bstruc)
if(nrow(Bstruc)!=xdim[2]){stop("Input 'Bstruc' must have the same number of rows as dim(X)[2]")}
if(ncol(Bstruc)!=nfac){stop("Input 'Bstruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Bstruc,1:2,class)))){stop("Input 'Bstruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
if(!is.null(Cstruc)){
Cstruc <- as.matrix(Cstruc)
if(nrow(Cstruc)!=xdim[3]){stop("Input 'Cstruc' must have the same number of rows as dim(X)[3]")}
if(ncol(Cstruc)!=nfac){stop("Input 'Cstruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Cstruc,1:2,class)))){stop("Input 'Cstruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
# check 'Amodes' and 'Bmodes' and 'Cmodes' inputs
if(any(const[1] == const.unimod) && !is.null(Amodes)){
Amodes <- as.matrix(Amodes)
if(nrow(Amodes) != 2L | ncol(Amodes) != nfac) stop("Input 'Amodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Amodes <- matrix(as.integer(Amodes), nrow = 2L, ncol = nfac)
if(any(Amodes < 1L)) stop("First row of 'Amodes' must contain integers greater than or equal to one.")
if(any(Amodes > xdim[1])) stop("Second row of 'Amodes' must contain integers less than or equal to dim(X)[1].")
if(any((Amodes[2,] - Amodes[1,]) < 0)) stop("Input 'Amodes' must satisfy: Amodes[1,r] <= Amodes[2,r]")
}
if(any(const[2] == const.unimod) && !is.null(Bmodes)){
Bmodes <- as.matrix(Bmodes)
if(nrow(Bmodes) != 2L | ncol(Bmodes) != nfac) stop("Input 'Bmodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Bmodes <- matrix(as.integer(Bmodes), nrow = 2L, ncol = nfac)
if(any(Bmodes < 1L)) stop("First row of 'Bmodes' must contain integers greater than or equal to one.")
if(any(Bmodes > xdim[2])) stop("Second row of 'Bmodes' must contain integers less than or equal to dim(X)[2].")
if(any((Bmodes[2,] - Bmodes[1,]) < 0)) stop("Input 'Bmodes' must satisfy: Bmodes[1,r] <= Bmodes[2,r]")
}
if(any(const[3] == const.unimod) && !is.null(Cmodes)){
Cmodes <- as.matrix(Cmodes)
if(nrow(Cmodes) != 2L | ncol(Cmodes) != nfac) stop("Input 'Cmodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Cmodes <- matrix(as.integer(Cmodes), nrow = 2L, ncol = nfac)
if(any(Cmodes < 1L)) stop("First row of 'Cmodes' must contain integers greater than or equal to one.")
if(any(Cmodes > xdim[3])) stop("Second row of 'Cmodes' must contain integers less than or equal to dim(X)[3].")
if(any((Cmodes[2,] - Cmodes[1,]) < 0)) stop("Input 'Cmodes' must satisfy: Cmodes[1,r] <= Cmodes[2,r]")
}
# check 'parallel' and 'cl' inputs
if(parallel && !any(class(cl)=="cluster")){
stop("Input 'cl' must be cluster (created by makeCluster) when parallel=TRUE \n See examples in documentation: ?parafac")
}
# parafac fitting
if(lxdim==3L){
if(parallel){
nstartlist <- vector("list",nstart)
nstartlist[1:nstart] <- nfac
if(missingdata){
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_3wayna",
data = X, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
} else {
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_3way",
data = X, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
} # end if(missingdata)
} else {
if(verbose) pbar <- txtProgressBar(min = 0, max = nstart, style = 3)
if(output[1] == "best"){
if(missingdata){
pfac <- parafac_3wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_3wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} else {
pfac <- parafac_3way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_3way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} # end if(missingdata)
} else {
pfaclist <- vector("list",nstart)
if(missingdata){
for(j in 1:nstart){
pfaclist[[j]] <- parafac_3wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} else {
for(j in 1:nstart){
pfaclist[[j]] <- parafac_3way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} # end if(missingdata)
} # end if(output[1] == "best")
if(verbose) close(pbar)
} # end if(parallel)
} else if(lxdim==4L){
# check 'Dfixed', 'Dstart', 'Dstruc', and 'Dmodes' inputs
if(!is.null(Dfixed)){
Dfixed <- as.matrix(Dfixed)
if(nrow(Dfixed)!=xdim[4]){stop("Input 'Dfixed' must have the same number of rows as dim(X)[4]")}
if(ncol(Dfixed)!=nfac){stop("Input 'Dfixed' must have 'nfac' columns")}
}
if(!is.null(Dstart)){
Dstart <- as.matrix(Dstart)
if(nrow(Dstart)!=xdim[4]){stop("Input 'Dstart' must have the same number of rows as dim(X)[4]")}
if(ncol(Dstart)!=nfac){stop("Input 'Dstart' must have 'nfac' columns")}
}
if(!is.null(Dstruc)){
Dstruc <- as.matrix(Dstruc)
if(nrow(Dstruc)!=xdim[4]){stop("Input 'Dstruc' must have the same number of rows as dim(X)[4]")}
if(ncol(Dstruc)!=nfac){stop("Input 'Dstruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Dstruc,1:2,class)))){stop("Input 'Dstruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
if(any(const[4] == const.unimod) && !is.null(Dmodes)){
Dmodes <- as.matrix(Dmodes)
if(nrow(Dmodes) != 2L | ncol(Dmodes) != nfac) stop("Input 'Dmodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Dmodes <- matrix(as.integer(Dmodes), nrow = 2L, ncol = nfac)
if(any(Dmodes < 1L)) stop("First row of 'Dmodes' must contain integers greater than or equal to one.")
if(any(Dmodes > xdim[4])) stop("Second row of 'Dmodes' must contain integers less than or equal to dim(X)[4].")
if(any((Dmodes[2,] - Dmodes[1,]) < 0)) stop("Input 'Dmodes' must satisfy: Dmodes[1,r] <= Dmodes[2,r]")
}
# fit models
if(parallel){
nstartlist <- vector("list",nstart)
nstartlist[1:nstart] <- nfac
if(missingdata){
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_4wayna", data = X, naid = naid,
const = const, control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
} else {
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_4way", data = X, xcx = xcx,
const = const, control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
} # end if(missingdata)
} else {
if(verbose) pbar <- txtProgressBar(min = 0, max = nstart, style = 3)
if(output[1] == "best"){
if(missingdata){
pfac <- parafac_4wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_4wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} else {
pfac <- parafac_4way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit,ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_4way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit,ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} # end if(missingdata)
} else {
pfaclist <- vector("list",nstart)
if(missingdata){
for(j in 1:nstart){
pfaclist[[j]] <- parafac_4wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} else {
for(j in 1:nstart){
pfaclist[[j]] <- parafac_4way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit,ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} # end if(missingdata)
} # end if(output[1] == "best")
if(verbose) close(pbar)
} # end if(parallel)
} # end if(lxdim==3L)
# output results
if(output[1] == "best"){
if(parallel){
SSE <- sapply(pfaclist,function(x) x$SSE)
pfac <- pfaclist[[which.min(SSE)]]
}
class(pfac) <- "parafac"
return(pfac)
} else {
pfaclist <- lapply(pfaclist, function(pfac) {
class(pfac) <- "parafac"
pfac
})
return(pfaclist)
}
} # end parafac.R
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parafac <-
function(X, nfac, nstart = 10, const = NULL, control = NULL,
Afixed = NULL, Bfixed = NULL, Cfixed = NULL, Dfixed = NULL,
Astart = NULL, Bstart = NULL, Cstart = NULL, Dstart = NULL,
Astruc = NULL, Bstruc = NULL, Cstruc = NULL, Dstruc = NULL,
Amodes = NULL, Bmodes = NULL, Cmodes = NULL, Dmodes = NULL,
maxit = 500, ctol = 1e-4, parallel = FALSE, cl = NULL,
output = c("best", "all"), verbose = TRUE, backfit = FALSE){
# 3-way or 4-way Parallel Factor Analysis (Parafac)
# via alternating least squares (ALS) with optional constraints
# Nathaniel E. Helwig (helwig@umn.edu)
# last updated: May 25, 2018
# check 'X' input
xdim <- dim(X)
lxdim <- length(xdim)
if((lxdim < 3L) | (lxdim > 4L)) stop("Input 'X' must be 3-way or 4-way array")
if(any(is.nan(X)) | any(is.infinite(X))) stop("Input 'X' cannot contain NaN or Inf values")
if(any(is.na(X))){
missingdata <- TRUE
naid <- which(is.na(X))
} else {
missingdata <- FALSE
xcx <- sumsq(X)
}
# check 'nfac' and 'nstart' inputs
nfac <- as.integer(nfac[1])
if(nfac<1L){stop("Input 'nfac' must be positive integer")}
nstart <- as.integer(nstart[1])
if(nstart<1L){stop("Input 'nstart' must be positive integer")}
# check 'maxit' and 'ctol' inputs
maxit <- as.integer(maxit[1])
if(maxit<1L){stop("Input 'maxit' must be positive integer")}
ctol <- as.numeric(ctol[1])
if(ctol<0L){stop("Input 'ctol' must be positive numeric")}
# const types: old, new, and spline
const.oldtypes <- c("uncons", "orthog", "nonneg",
"unismo", "monsmo", "smoper", "smooth")
const.newtypes <- c("uncons", "nonneg", "period", "pernon",
"smooth", "smonon", "smoper", "smpeno",
"orthog", "ortnon", "ortsmo", "orsmpe",
"moninc", "monnon", "monsmo", "mosmno",
"unimod", "uninon", "uniper", "unpeno",
"unismo", "unsmno", "unsmpe", "unsmpn")
const.smooth <- c("smooth", "smonon", "smoper", "smpeno",
"ortsmo", "orsmpe", "monsmo", "mosmno",
"unismo", "unsmno", "unsmpe", "unsmpn")
const.unimod <- c("unimod", "uninon", "uniper", "unpeno",
"unismo", "unsmno", "unsmpe", "unsmpn")
# check 'const' input
if(is.null(const)){
const <- rep("uncons", lxdim)
} else {
if(length(const) != lxdim) stop("Input 'const' must be ",lxdim," element vector specifying constraint for each mode")
if(is.integer(const) | is.numeric(const)){
const <- as.integer(const)
if(any(is.na(const))) const[is.na(const)] <- 0L
if(any(const < 0L) | any(const > 6L)) stop("Input 'const' must contain characters (preferred) or integers between 0 and 6.")
const <- const.oldtypes[const + 1L]
} else {
const <- as.character(const)
if(any(is.na(const))) const[is.na(const)] <- "uncons"
cid <- pmatch(const, const.newtypes, duplicates.ok = TRUE)
if(any(is.na(cid))) stop("Input 'const' must be a character vector of length ",lxdim,"\n with each element matching one of the 24 available options.")
const <- const.newtypes[cid]
}
} # end if(is.null(const))
# check 'control' input
convars <- list(const=const, df=control$df, degree=control$degree, intercept=control$intercept)
control <- do.call("const.control", convars)
for(j in 1:length(const)){
if(any(const[j] == const.smooth)){
if(control$df[j] >= xdim[j]) {
warning(paste0("Input control$df[",j,"] = ",control$df[j]," >= dim(X)[",j,"] = ",xdim[j],"\nResetting control$df[",j,"] = ",xdim[j]-1,"."))
control$df[j] <- xdim[j] - 1
}
}
}
# check 'Afixed' and 'Bfixed' and 'Cfixed' inputs
if(!is.null(Afixed)){
Afixed <- as.matrix(Afixed)
if(nrow(Afixed)!=xdim[1]){stop("Input 'Afixed' must have the same number of rows as dim(X)[1]")}
if(ncol(Afixed)!=nfac){stop("Input 'Afixed' must have 'nfac' columns")}
}
if(!is.null(Bfixed)){
Bfixed <- as.matrix(Bfixed)
if(nrow(Bfixed)!=xdim[2]){stop("Input 'Bfixed' must have the same number of rows as dim(X)[2]")}
if(ncol(Bfixed)!=nfac){stop("Input 'Bfixed' must have 'nfac' columns")}
}
if(!is.null(Cfixed)){
Cfixed <- as.matrix(Cfixed)
if(nrow(Cfixed)!=xdim[3]){stop("Input 'Cfixed' must have the same number of rows as dim(X)[3]")}
if(ncol(Cfixed)!=nfac){stop("Input 'Cfixed' must have 'nfac' columns")}
}
# check 'Astart' and 'Bstart' and 'Cstart' inputs
if(!is.null(Astart)){
Astart <- as.matrix(Astart)
if(nrow(Astart)!=xdim[1]){stop("Input 'Astart' must have the same number of rows as dim(X)[1]")}
if(ncol(Astart)!=nfac){stop("Input 'Astart' must have 'nfac' columns")}
}
if(!is.null(Bstart)){
Bstart <- as.matrix(Bstart)
if(nrow(Bstart)!=xdim[2]){stop("Input 'Bstart' must have the same number of rows as dim(X)[2]")}
if(ncol(Bstart)!=nfac){stop("Input 'Bstart' must have 'nfac' columns")}
}
if(!is.null(Cstart)){
Cstart <- as.matrix(Cstart)
if(nrow(Cstart)!=xdim[3]){stop("Input 'Cstart' must have the same number of rows as dim(X)[3]")}
if(ncol(Cstart)!=nfac){stop("Input 'Cstart' must have 'nfac' columns")}
}
# check 'Astruc' and 'Bstruc' and 'Cstruc' inputs
if(!is.null(Astruc)){
Astruc <- as.matrix(Astruc)
if(nrow(Astruc)!=xdim[1]){stop("Input 'Astruc' must have the same number of rows as dim(X)[1]")}
if(ncol(Astruc)!=nfac){stop("Input 'Astruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Astruc,1:2,class)))){stop("Input 'Astruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
if(!is.null(Bstruc)){
Bstruc <- as.matrix(Bstruc)
if(nrow(Bstruc)!=xdim[2]){stop("Input 'Bstruc' must have the same number of rows as dim(X)[2]")}
if(ncol(Bstruc)!=nfac){stop("Input 'Bstruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Bstruc,1:2,class)))){stop("Input 'Bstruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
if(!is.null(Cstruc)){
Cstruc <- as.matrix(Cstruc)
if(nrow(Cstruc)!=xdim[3]){stop("Input 'Cstruc' must have the same number of rows as dim(X)[3]")}
if(ncol(Cstruc)!=nfac){stop("Input 'Cstruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Cstruc,1:2,class)))){stop("Input 'Cstruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
# check 'Amodes' and 'Bmodes' and 'Cmodes' inputs
if(any(const[1] == const.unimod) && !is.null(Amodes)){
Amodes <- as.matrix(Amodes)
if(nrow(Amodes) != 2L | ncol(Amodes) != nfac) stop("Input 'Amodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Amodes <- matrix(as.integer(Amodes), nrow = 2L, ncol = nfac)
if(any(Amodes < 1L)) stop("First row of 'Amodes' must contain integers greater than or equal to one.")
if(any(Amodes > xdim[1])) stop("Second row of 'Amodes' must contain integers less than or equal to dim(X)[1].")
if(any((Amodes[2,] - Amodes[1,]) < 0)) stop("Input 'Amodes' must satisfy: Amodes[1,r] <= Amodes[2,r]")
}
if(any(const[2] == const.unimod) && !is.null(Bmodes)){
Bmodes <- as.matrix(Bmodes)
if(nrow(Bmodes) != 2L | ncol(Bmodes) != nfac) stop("Input 'Bmodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Bmodes <- matrix(as.integer(Bmodes), nrow = 2L, ncol = nfac)
if(any(Bmodes < 1L)) stop("First row of 'Bmodes' must contain integers greater than or equal to one.")
if(any(Bmodes > xdim[2])) stop("Second row of 'Bmodes' must contain integers less than or equal to dim(X)[2].")
if(any((Bmodes[2,] - Bmodes[1,]) < 0)) stop("Input 'Bmodes' must satisfy: Bmodes[1,r] <= Bmodes[2,r]")
}
if(any(const[3] == const.unimod) && !is.null(Cmodes)){
Cmodes <- as.matrix(Cmodes)
if(nrow(Cmodes) != 2L | ncol(Cmodes) != nfac) stop("Input 'Cmodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Cmodes <- matrix(as.integer(Cmodes), nrow = 2L, ncol = nfac)
if(any(Cmodes < 1L)) stop("First row of 'Cmodes' must contain integers greater than or equal to one.")
if(any(Cmodes > xdim[3])) stop("Second row of 'Cmodes' must contain integers less than or equal to dim(X)[3].")
if(any((Cmodes[2,] - Cmodes[1,]) < 0)) stop("Input 'Cmodes' must satisfy: Cmodes[1,r] <= Cmodes[2,r]")
}
# check 'parallel' and 'cl' inputs
if(parallel && !any(class(cl)=="cluster")){
stop("Input 'cl' must be cluster (created by makeCluster) when parallel=TRUE \n See examples in documentation: ?parafac")
}
# parafac fitting
if(lxdim==3L){
if(parallel){
nstartlist <- vector("list",nstart)
nstartlist[1:nstart] <- nfac
if(missingdata){
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_3wayna",
data = X, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
} else {
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_3way",
data = X, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
} # end if(missingdata)
} else {
if(verbose) pbar <- txtProgressBar(min = 0, max = nstart, style = 3)
if(output[1] == "best"){
if(missingdata){
pfac <- parafac_3wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_3wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} else {
pfac <- parafac_3way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_3way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} # end if(missingdata)
} else {
pfaclist <- vector("list",nstart)
if(missingdata){
for(j in 1:nstart){
pfaclist[[j]] <- parafac_3wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} else {
for(j in 1:nstart){
pfaclist[[j]] <- parafac_3way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} # end if(missingdata)
} # end if(output[1] == "best")
if(verbose) close(pbar)
} # end if(parallel)
} else if(lxdim==4L){
# check 'Dfixed', 'Dstart', 'Dstruc', and 'Dmodes' inputs
if(!is.null(Dfixed)){
Dfixed <- as.matrix(Dfixed)
if(nrow(Dfixed)!=xdim[4]){stop("Input 'Dfixed' must have the same number of rows as dim(X)[4]")}
if(ncol(Dfixed)!=nfac){stop("Input 'Dfixed' must have 'nfac' columns")}
}
if(!is.null(Dstart)){
Dstart <- as.matrix(Dstart)
if(nrow(Dstart)!=xdim[4]){stop("Input 'Dstart' must have the same number of rows as dim(X)[4]")}
if(ncol(Dstart)!=nfac){stop("Input 'Dstart' must have 'nfac' columns")}
}
if(!is.null(Dstruc)){
Dstruc <- as.matrix(Dstruc)
if(nrow(Dstruc)!=xdim[4]){stop("Input 'Dstruc' must have the same number of rows as dim(X)[4]")}
if(ncol(Dstruc)!=nfac){stop("Input 'Dstruc' must have 'nfac' columns")}
if(any("logical"!=c(apply(Dstruc,1:2,class)))){stop("Input 'Dstruc' must be a matrix with logical (TRUE/FALSE) entries.")}
}
if(any(const[4] == const.unimod) && !is.null(Dmodes)){
Dmodes <- as.matrix(Dmodes)
if(nrow(Dmodes) != 2L | ncol(Dmodes) != nfac) stop("Input 'Dmodes' must be a 2 x nfac matrix giving the\n minimum (row 1) and maximum (row 2) allowable mode for each factor.")
Dmodes <- matrix(as.integer(Dmodes), nrow = 2L, ncol = nfac)
if(any(Dmodes < 1L)) stop("First row of 'Dmodes' must contain integers greater than or equal to one.")
if(any(Dmodes > xdim[4])) stop("Second row of 'Dmodes' must contain integers less than or equal to dim(X)[4].")
if(any((Dmodes[2,] - Dmodes[1,]) < 0)) stop("Input 'Dmodes' must satisfy: Dmodes[1,r] <= Dmodes[2,r]")
}
# fit models
if(parallel){
nstartlist <- vector("list",nstart)
nstartlist[1:nstart] <- nfac
if(missingdata){
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_4wayna", data = X, naid = naid,
const = const, control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
} else {
pfaclist <- parLapply(cl = cl, X = nstartlist, fun = "parafac_4way", data = X, xcx = xcx,
const = const, control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
} # end if(missingdata)
} else {
if(verbose) pbar <- txtProgressBar(min = 0, max = nstart, style = 3)
if(output[1] == "best"){
if(missingdata){
pfac <- parafac_4wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_4wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} else {
pfac <- parafac_4way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit,ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, 1)
if(nstart > 1L){
for(j in 2:nstart){
pnew <- parafac_4way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit,ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(pnew$SSE < pfac$SSE) pfac <- pnew
if(verbose) setTxtProgressBar(pbar, j)
} # end for(j in 2:nstart)
} # end if(nstart > 1L)
} # end if(missingdata)
} else {
pfaclist <- vector("list",nstart)
if(missingdata){
for(j in 1:nstart){
pfaclist[[j]] <- parafac_4wayna(data = X, nfac = nfac, naid = naid, const = const,
control = control, maxit = maxit, ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} else {
for(j in 1:nstart){
pfaclist[[j]] <- parafac_4way(data = X, nfac = nfac, xcx = xcx, const = const,
control = control, maxit = maxit,ctol = ctol,
Afixed = Afixed, Bfixed = Bfixed, Cfixed = Cfixed, Dfixed = Dfixed,
Astart = Astart, Bstart = Bstart, Cstart = Cstart, Dstart = Dstart,
Astruc = Astruc, Bstruc = Bstruc, Cstruc = Cstruc, Dstruc = Dstruc,
Amodes = Amodes, Bmodes = Bmodes, Cmodes = Cmodes, Dmodes = Dmodes,
backfit = backfit)
if(verbose) setTxtProgressBar(pbar, j)
}
} # end if(missingdata)
} # end if(output[1] == "best")
if(verbose) close(pbar)
} # end if(parallel)
} # end if(lxdim==3L)
# output results
if(output[1] == "best"){
if(parallel){
SSE <- sapply(pfaclist,function(x) x$SSE)
pfac <- pfaclist[[which.min(SSE)]]
}
class(pfac) <- "parafac"
return(pfac)
} else {
pfaclist <- lapply(pfaclist, function(pfac) {
class(pfac) <- "parafac"
pfac
})
return(pfaclist)
}
} # end parafac.R
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