(Truncated-)Higher-order SVD
Higher-order SVD of a K-Tensor. Write the K-Tensor as a (m-mode) product of a core Tensor (possibly smaller modes) and K orthogonal factor matrices. Truncations can be specified via ranks (making them smaller than the original modes of the K-Tensor will result in a truncation). For the mathematical details on HOSVD, consult Lathauwer et. al. (2000).
hosvd(tnsr, ranks = NULL)
tnsr |
Tensor with K modes |
ranks |
a vector of desired modes in the output core tensor, default is |
A progress bar is included to help monitor operations on large tensors.
a list containing the following:
Zcore tensor with modes speficied by ranks
Ua list of orthogonal matrices, one for each mode
estestimate of tnsr after compression
fnorm_residthe Frobenius norm of the error fnorm(est-tnsr) - if there was no truncation, then this is on the order of mach_eps * fnorm.
The length of ranks must match tnsr@num_modes.
L. Lathauwer, B.Moor, J. Vanderwalle "A multilinear singular value decomposition". Journal of Matrix Analysis and Applications 2000.
tnsr <- rand_tensor(c(6,7,8)) hosvdD <- hosvd(tnsr) plot(hosvdD$fnorm_resid) hosvdD2 <- hosvd(tnsr,ranks=c(3,3,4)) plot(hosvdD2$fnorm_resid)
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