56 lines
2.0 KiB
R
56 lines
2.0 KiB
R
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#' A simple higher order (multi-way) canonical correlation analysis.
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#'
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#' @param X multi-dimensional array
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#' @param Y multi-dimensional array with the same nr. of dimensions and equal
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#' sample axis to `X`.
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#' @param sample.axis integer indicationg which axis enumerates observations
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#'
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#' @export
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HOCCA <- function(X, Y, sample.axis = length(dim(X)), centerX = TRUE, centerY = TRUE) {
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# ensure sample axis is the last axis
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if (!missing(sample.axis)) {
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modes <- seq_along(dim(X))[-sample.axis]
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X <- aperm(X, c(modes, sample.axis))
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Y <- aperm(Y, c(modes, sample.axis))
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}
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modes <- seq_len(length(dim(X)) - 1L)
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dimX <- head(dim(X), -1L)
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dimF <- head(dim(F), -1L)
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sample.size <- tail(dim(X), 1L)
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# center `X` and `Y`
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if (centerX) {
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X <- X - as.vector(rowMeans(X, dims = length(dim(X)) - 1L))
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}
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if (centerY) {
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Y <- Y - as.vector(rowMeans(Y, dims = length(dim(Y)) - 1L))
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}
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# estimate marginal covariance matrices
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CovXX <- Map(function(mode) mcrossprod(X, mode = mode) / prod(dim(X)[-mode]), modes)
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CovYY <- Map(function(mode) mcrossprod(Y, mode = mode) / prod(dim(Y)[-mode]), modes)
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# and the "covariance tensor"
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CovXY <- array(tcrossprod(mat(X, modes), mat(Y, modes)) / sample.size, c(dimX, dimF))
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# Compute standardized X and Y correlation tensor
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SCovXY <- mlm(CovXY, Map(matpow, c(CovXX, CovYY), -1 / 2))
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# mode-wise canonical correlation directions
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hosvd <- HOSVD(SCovXY, nu = rep(pmin(dimX, dimF), 2L))
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dirsX <- hosvd$Us[modes]
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dirsY <- hosvd$Us[modes + length(modes)]
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list(dirsX = dirsX, dirsY = dirsY)
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}
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# c(dirsX, dirsY) %<-% HOCCA(X, F)
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# B.hocca <- Reduce(kronecker, rev(Map(tcrossprod, dirsX, dirsY)))
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# dist.subspace(B.true, B.hocca, normalize = TRUE)
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# dist.subspace(B.true, Reduce(kronecker, rev(dirsX)), normalize = TRUE)
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# cca <- cancor(mat(X, 4), mat(F, 4))
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# B.cca <- tcrossprod(cca$xcoef[, prod(dim(X)[-4])], cca$xcoef[, prod(dim(F)[-4])])
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# dist.subspace(B.true, cca$xcoef[, prod(dim(X)[-4])], normalize = TRUE)
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