Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion

06/10/2016
by   Ming Yuan, et al.
0

In this paper, we investigate the sample size requirement for a general class of nuclear norm minimization methods for higher order tensor completion. We introduce a class of tensor norms by allowing for different levels of coherence, which allows us to leverage the incoherence of a tensor. In particular, we show that a kth order tensor of rank r and dimension d×...× d can be recovered perfectly from as few as O((r^(k-1)/2d^3/2+r^k-1d)((d))^2) uniformly sampled entries through an appropriate incoherent nuclear norm minimization. Our results demonstrate some key differences between completing a matrix and a higher order tensor: They not only point to potential room for improvement over the usual nuclear norm minimization but also highlight the importance of explicitly accounting for incoherence, when dealing with higher order tensors.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/07/2014

On Tensor Completion via Nuclear Norm Minimization

Many problems can be formulated as recovering a low-rank tensor. Althoug...
research
07/25/2017

Scaled Nuclear Norm Minimization for Low-Rank Tensor Completion

Minimizing the nuclear norm of a matrix has been shown to be very effici...
research
09/04/2019

Spectral Norm and Nuclear Norm of a Third Order Tensor

The spectral norm and the nuclear norm of a third order tensor play an i...
research
02/22/2017

On Polynomial Time Methods for Exact Low Rank Tensor Completion

In this paper, we investigate the sample size requirement for exact reco...
research
10/31/2017

Effective Tensor Sketching via Sparsification

In this paper, we investigate effective sketching schemes via sparsifica...
research
08/01/2017

On Tensor Train Rank Minimization: Statistical Efficiency and Scalable Algorithm

Tensor train (TT) decomposition provides a space-efficient representatio...
research
07/10/2019

Higher-order ergodicity coefficients for stochastic tensors

Ergodicity coefficients for stochastic matrices provide valuable upper b...

Please sign up or login with your details

Forgot password? Click here to reset