83 lines
2.8 KiB
R
83 lines
2.8 KiB
R
#' Per mode (axis) alternating least squares estimate
|
|
#'
|
|
#' @param sample.axis index of the sample mode, a.k.a. observation axis index
|
|
#'
|
|
#' @export
|
|
kpir.ls <- function(X, Fy, max.iter = 20L, sample.axis = 1L,
|
|
eps = sqrt(.Machine$double.eps), center = TRUE, logger = NULL
|
|
) {
|
|
### Step 0: Setup/Initialization
|
|
if (!is.array(Fy)) {
|
|
# scalar response case (add new axis of size 1)
|
|
dim(Fy) <- ifelse(seq_along(dim(X)) == sample.axis, dim(X)[sample.axis], 1L)
|
|
}
|
|
# Check dimensions and matching of axis (tensor order)
|
|
stopifnot(exprs = {
|
|
length(dim(X)) == length(dim(Fy))
|
|
dim(X)[sample.axis] == dim(Fy)[sample.axis]
|
|
})
|
|
# warn about occurence of an axis without reduction
|
|
if (any(dim(Fy)[-sample.axis] >= dim(X)[-sample.axis])) {
|
|
warning("Degenerate case 'any(dim(Fy)[-sample.axis] >= dim(X)[-sample.axis])'")
|
|
}
|
|
|
|
# mode index sequence (exclude sample mode, a.k.a. observation axis)
|
|
modes <- seq_along(dim(X))[-sample.axis]
|
|
n <- dim(X)[sample.axis] # observation count (scalar)
|
|
p <- dim(X)[-sample.axis] # predictor dimensions (vector)
|
|
|
|
if (center) {
|
|
# Means for X and Fy (a.k.a. sum elements over the sample axis)
|
|
meanX <- apply(X, modes, mean, simplify = TRUE)
|
|
meanFy <- apply(Fy, modes, mean, simplify = TRUE)
|
|
# Center both X and Fy
|
|
X <- sweep(X, modes, meanX)
|
|
Fy <- sweep(Fy, modes, meanFy)
|
|
} else {
|
|
meanX <- meanFy <- NA
|
|
}
|
|
|
|
|
|
### Step 1: initial per mode estimates
|
|
alphas <- Map(function(mode, ncol) {
|
|
La.svd(mcrossprod(X, mode = mode), ncol)$u
|
|
}, modes, dim(Fy)[modes])
|
|
|
|
|
|
### Step 2: iterate per mode (axis) least squares estimates
|
|
for (iter in seq_len(max.iter)) {
|
|
|
|
# Invoke logger for previous iterate
|
|
if (is.function(logger)) {
|
|
logger("ls", iter - 1L, alphas)
|
|
}
|
|
|
|
# cyclic iterate over modes
|
|
for (j in seq_along(modes)) {
|
|
# least squares solution for `alpha_j | alpha_i, i != j`
|
|
Z <- mlm(Fy, alphas[-j], modes = modes[-j])
|
|
alphas[[j]] <- t(solve(
|
|
mcrossprod(Z, Z, modes[j]), mcrossprod(Z, X, modes[j])
|
|
))
|
|
}
|
|
|
|
# TODO: add some kind of break condition
|
|
}
|
|
|
|
### Step 3: Moment estimates for `Delta_i`
|
|
# Residuals
|
|
R <- X - mlm(Fy, alphas, modes = modes)
|
|
# Moment estimates for `Delta_i`s
|
|
Deltas <- Map(mcrossprod, list(R), mode = modes)
|
|
Deltas <- Map(`*`, p / (n * prod(p)), Deltas)
|
|
|
|
# Call logger with final results (including Deltas)
|
|
if (is.function(logger)) {
|
|
logger("ls", iter, alphas, Deltas)
|
|
}
|
|
|
|
list(alphas = structure(alphas, names = as.character(modes)),
|
|
Deltas = structure(Deltas, names = as.character(modes)),
|
|
meanX = meanX, meanFy = meanFy)
|
|
}
|