View source: R/tensor_decomp.R
hosvd | R Documentation |
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:
Z
core tensor with modes speficied by ranks
U
a list of orthogonal matrices, one for each mode
est
estimate of tnsr
after compression
fnorm_resid
the 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. Vandewalle, "A multilinear singular value decomposition". Journal of Matrix Analysis and Applications 2000, Vol. 21, No. 4, pp. 1253–1278.
tucker
tnsr <- rand_tensor(c(6,7,8))
hosvdD <-hosvd(tnsr)
hosvdD$fnorm_resid
hosvdD2 <-hosvd(tnsr,ranks=c(3,3,4))
hosvdD2$fnorm_resid
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