add: mlm, kpir_ls

This commit is contained in:
Daniel Kapla 2022-05-11 17:26:37 +02:00
parent 36dd08c7c9
commit 7c33cc152f
4 changed files with 126 additions and 1 deletions

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@ -24,6 +24,7 @@ export(matrixImage)
export(mcrossprod)
export(reduce)
export(rowKronecker)
export(rtensornorm)
export(tensor_predictor)
export(ttm)
import(stats)

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@ -40,7 +40,7 @@ dist.subspace <- function (A, B, is.ortho = FALSE, normalize = FALSE,
if (normalize) {
rankSum <- ncol(A) + ncol(B)
c <- 1 / sqrt(min(rankSum, 2 * nrow(A) - rankSum))
c <- 1 / sqrt(max(1, min(rankSum, 2 * nrow(A) - rankSum)))
} else {
c <- sqrt(2)
}

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@ -0,0 +1,53 @@
#' Per mode (axis) alternating least squares estimate
#'
#' @param sample.mode index of the sample mode, a.k.a. observation axis index
#'
#' @export
kpir.ls <- function(X, Fy, max.iter = 20L, sample.mode = 1L,
eps = .Machine$double.eps, logger = NULL
) {
# Check if X and Fy have same number of observations
if (!is.array(Fy)) {
# scalar response case (add new axis of size 1)
dim(Fy) <- local({
dims <- rep(1, length(dim(X)))
dims[sample.mode] <- length(Fy)
dims
})
} else {
stopifnot(dim(X)[sample.mode] == dim(Fy)[sample.mode])
}
# and check shape
stopifnot(length(X) == length(Fy))
# mode index sequence (exclude sample mode, a.k.a. observation axis)
modes <- seq_along(dim(X))[-sample.mode]
### Step 1: initial per mode estimates
alphas <- Map(function(mode, ncol) {
La.svd(mcrossprod(X, mode), ncol)$u
}, modes, dim(Fy)[modes])
# Call history callback (logger) before the first iteration
if (is.function(logger)) { logger(0L, alphas) }
### Step 2: iterate per mode (axis) least squares estimates
for (iter in seq_len(max.iter)) {
# 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, j), tcrossprod(mat(Z, j), mat(X, j))))
# TODO: alphas[[j]] <- t(solve(mcrossprod(Z, j), mcrossprod(Z, X, j)))
}
# Call logger (invoke history callback)
if (is.function(logger)) { logger(iter, alphas) }
# TODO: add some kind of break condition
}
}

71
tensorPredictors/R/mlm.R Normal file
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@ -0,0 +1,71 @@
#' Multi Linear Multiplication
#'
#' C = A x { B1, ..., Br }
#'
#' @param A tensor (multi-linear array)
#' @param B matrix or list of matrices
#' @param ... further matrices, concatenated with \code{B}
#' @param modes integer sequence of the same length as number of matrices
#' supplied (in \code{B} and \code{...})
#'
#' @examples
#' # general usage
#' dimA <- c(3, 17, 19, 2)
#' dimC <- c(7, 11, 13, 5)
#' A <- array(rnorm(prod(dimA)), dim = dimA)
#' B <- Map(function(p, q) matrix(rnorm(p * q), p, q), dimC, dimA)
#' C1 <- mlm(A, B)
#' C2 <- mlm(A, B[[1]], B[[2]], B[[3]], B[[4]])
#' C3 <- mlm(A, B[[3]], B[[1]], B[[2]], B[[4]], modes = c(3, 1, 2, 4))
#' C4 <- mlm(A, B[1:3], B[[4]])
#' stopifnot(all.equal(C1, C2))
#' stopifnot(all.equal(C1, C3))
#' stopifnot(all.equal(C1, C4))
#'
#' # selected modes
#' C1 <- mlm(A, B, modes = 2:3)
#' C2 <- mlm(A, B[[2]], B[[3]], modes = 2:3)
#' C3 <- ttm(ttm(A, B[[2]], 2), B[[3]], 3)
#' stopifnot(all.equal(C1, C2))
#' stopifnot(all.equal(C1, C3))
#'
#' # analog to matrix multiplication
#' A <- matrix(rnorm( 6), 2, 3)
#' B <- matrix(rnorm(12), 3, 4)
#' C <- matrix(rnorm(20), 4, 5)
#' stopifnot(all.equal(
#' A %*% B %*% t(C),
#' mlm(B, list(A, C))
#' ))
#'
#' # usage with repeated modes (non commutative)
#' dimA <- c(3, 17, 19, 2)
#' A <- array(rnorm(prod(dimA)), dim = dimA)
#' B1 <- matrix(rnorm(9), 3, 3)
#' B2 <- matrix(rnorm(9), 3, 3)
#' C <- matrix(rnorm(4), 2, 2)
#' # same modes do NOT commute
#' all.equal(
#' mlm(A, B1, B2, C, modes = c(1, 1, 4)), # NOT equal!
#' mlm(A, B2, B1, C, modes = c(1, 1, 4))
#' )
#' # but different modes do commute
#' P1 <- mlm(A, C, B1, B2, modes = c(4, 1, 1))
#' P2 <- mlm(A, B1, C, B2, modes = c(1, 4, 1))
#' P3 <- mlm(A, B1, B2, C, modes = c(1, 1, 4))
#' stopifnot(all.equal(P1, P2))
#' stopifnot(all.equal(P1, P3))
#'
#' @export
mlm <- function(A, B, ..., modes = seq_along(B)) {
# Collect all matrices in `B`
B <- c(if (is.matrix(B)) list(B) else B, list(...))
# iteratively apply Tensor Times Matrix multiplication over modes
for (i in seq_along(modes)) {
A <- ttm(A, B[[i]], modes[i])
}
# return result tensor
A
}