I've placed some
R code on Github that is useful for working with higher-order spectral estimators. These estimators are based on the higher-order singular value decomposition of De Lathauwer et. al.  and are useful when your data exhibit tensor-specific structure, such as having approximately low multilinear rank. This code will allow you to:
All details of these methods may be found in
I also provide a vignette that demonstrates how to fit the truncated HOSVD and the mode-specific soft-thresholding estimators.
You can download the package by typing in
install.packages(c("tensr", "softImpute", "RMTstat", "devtools"))
These scripts were created and are maintained by David Gerard.
Please provide us with questions or comments: David Gerard (dcgerard) or Peter Hoff (pdhoff) -- @uchicago.edu and @uw.edu, respectively.
Lieven De Lathauwer, Bart De Moor, and Joos Vandewalle. A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl., 21(4):1253–1278 (electronic), 2000. ISSN 0895-4798. doi: 10.1137/S0895479896305696. [Link]
Sylvain Sardy. Smooth blockwise iterative thresholding: a smooth fixed point estimator based on the likelihood’s block gradient. J. Amer. Statist. Assoc., 107(498):800–813, 2012. ISSN 0162-1459. doi: 10.1080/01621459.2012.664527. [Link]