52 lines
1.9 KiB
R
52 lines
1.9 KiB
R
#' Mode wise Covariance Estimates
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#'
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#' Estimates Covariances \eqn{\Sigma_k}{Sigma_k} for each mode \eqn{k}.
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#' This is equivalent to assuming a Kronecker structured Covariance
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#'
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#' \deqn{\Sigma = \Sigma_r\otimes ... \otimes\Sigma_1}{%
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#' Sigma = Sigma_r %x% ... %x% Sigma_1}
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#'
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#' where \eqn{\Sigma}{Sigma} is the Covariance \eqn{cov(vec(X))} of the
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#' vectorized variables. This function estimates the Kronecerk components
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#' \eqn{\Sigma_k}{Sigma_k}.
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#'
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#' @param X multi-dimensional array
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#' @param sample.axis observation axis index
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#' @param center logical, if `TRUE` (the default) compute the centered second
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#' moment, that is, the mode-wise covariances. Otherwise, the raw second moment
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#' of each mode is computed. This is specifically usefull in case `X` is
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#' already centered.
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#'
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#' @export
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mcov <- function(X, sample.axis = length(dim(X)), center = TRUE) {
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# observation modes (axis indices)
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modes <- seq_along(dim(X))[-sample.axis]
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# observation dimensions
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p <- dim(X)[modes]
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# observation tensor order
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r <- length(p)
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# ensure observations are on the last mode
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if (sample.axis != r + 1L) {
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X <- aperm(X, c(modes, sample.axis))
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}
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# centering: X <- X - E[X]
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if (center) {
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X <- X - c(rowMeans(X, dims = r))
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}
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# unscaled covariances for each mode
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Sigmas <- .mapply(mcrossprod, list(mode = seq_len(r)), MoreArgs = list(X))
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# scale by per mode "sample" size
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Sigmas <- .mapply(`*`, list(Sigmas, p / prod(dim(X))), NULL)
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# estimate trace of Kronecker product of covariances
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tr.est <- prod(p) * mean(X^2)
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# as well as the current trace of the unscaled covariances
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tr.Sigmas <- prod(unlist(.mapply(function(S) sum(diag(S)), list(Sigmas), NULL)))
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# Scale each mode Covariance to match the estimated Kronecker product scale
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.mapply(`*`, list(Sigmas), MoreArgs = list((tr.est / tr.Sigmas)^(1 / r)))
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}
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