37 lines
1.3 KiB
R
37 lines
1.3 KiB
R
#' Higher Order Principal Component Analysis
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#'
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#' @param X multi-dimensional array (at least a matrix)
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#' @param npc Number of Principal Components for each axis, if not specified
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#' its the maximum
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#' @param sample.axis index of the sample mode, a.k.a. observation axis index
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#'
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#' @return list of matrices, each entry are the first PCs of the corresponding
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#' axis. The `i`'th entry are the `npc[i]` first Principal Components of the
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#' `i`th axis excluding the sample axis.
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#'
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#' @export
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HOPCA <- function(X, npc = dim(X)[-sample.axis], sample.axis = 1L, use.C = FALSE) {
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# observation index numbers (all axis except the sample axis)
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modes <- seq_along(dim(X))[-sample.axis]
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# Mean (a.k.a. sum elements over the sample axis)
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mu <- apply(X, modes, mean, simplify = TRUE)
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# Center `X` by subtraction of the mean `mu` from each observation
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X.centered <- sweep(X, modes, mu)
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# PCA for each mode (axis)
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PCs <- Map(function(i) {
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La.svd(mcrossprod(X.centered, mode = modes[i]), npc[i], 0)$u
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}, seq_along(modes))
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# Set names if any
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if (!is.null(dimnames(X))) {
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names(PCs) <- names(dimnames(X)[-sample.axis])
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for (i in seq_along(modes)) {
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dimnames(PCs[[i]]) <- list(dimnames(X)[-sample.axis][[i]], NULL)
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}
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}
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PCs
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}
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