# The $\ell_\infty$ Perturbation of HOSVD and Low Rank Tensor Denoising

• Published 2017 in ArXiv

#### Abstract

The higher order singular value decomposition (HOSVD) of tensors is a generalization of matrix SVD. The perturbation analysis of HOSVD under random noise is more delicate than its matrix counterpart. Recent progress has been made in Richard and Montanari [2014], Zhang and Xia [2017] and Liu et al. [2017] demonstrating that minimax optimal singular spaces… (More)

### Cite this paper

@article{Xia2017TheP, title={The \$\ell_\infty\$ Perturbation of HOSVD and Low Rank Tensor Denoising}, author={Dong Xia and Fan Zhou}, journal={CoRR}, year={2017}, volume={abs/1707.01207} }