A non-convex tensor rank approximation for tensor completion

Ji, Teng-Yu; Huang, Ting‐Zhu; Zhao, Xi-Le; Ma, Tianhui; Deng, Liang-Jian

doi:10.1016/j.apm.2017.04.002

Cited by 88 publications

(29 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Output: recovered tensor X 1 Initialize these variables H 0 n = M 0 n = 0, Y 0 n = Λ 0 n = 0, P Ω X 0 = P Ω (T ) , µ max = 10 10 , max iter = 500, η n = ε = 10 −6 , ρ = 1.05, µ 0 1 = µ 0 2 = 10 −4 , α, λ; 2 while not converged do = ρµ k 2 . 9 end [14]. Our model is implemented by the Tensor Toolbox for MATLAB 1 .…”

Section: Methodsmentioning

confidence: 99%

“…In order to overcome these limitations, a nonconvex rank approximation has been considered by Zhao et al [12] where the log-determinant (LogDet) function is used to approximate the rank function. The effectiveness of LogDet has been widely verified in several applications, such as subspace clustering [13], recommender system [12], and tensor completion [14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spatially Regularized Low Rank Tensor Optimization for Visual Data Completion

Gao

Shi

Wang

2018

2018 25th IEEE International Conference on Image Processing (ICIP)

View full text Add to dashboard Cite

Low-rank tensor completion is a recent method for estimating the values of the missing elements in tensor data by minimizing the tensor rank. However, with only the low rank prior, the local piecewise smooth structure that is important for visual data is not used effectively. To address this problem, we define a new spatial regularization S-norm for tensor completion in order to exploit the local spatial smoothness structure of visual data. More specifically, we introduce the S-norm to the tensor completion model based on a non-convex LogDet function. The S-norm helps to drive the neighborhood elements towards similar values. We utilize the Alternating Direction Method of Multiplier (ADMM) to optimize the proposed model. Experimental results in visual data demonstrate that our method outperforms the state-of-the-art tensor completion models.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatially Regularized Low Rank Tensor Optimization for Visual Data Completion

Gao

Shi

Wang

2018

2018 25th IEEE International Conference on Image Processing (ICIP)

View full text Add to dashboard Cite

show abstract

“…Then we incorporate t-SVD with the alternating direction method of multipliers (ADMM) [30,31,36,37,45] to solve the proposed model as shown in Algorithm 1. The iteration is ended if the error of two successive iterations is smaller than a constant ε, which is usually sufficiently small.…”

Section: Non-convex Low-rank Tensor Completionmentioning

confidence: 99%

Hyperspectral Image Recovery Using Non-Convex Low-Rank Tensor Approximation

Liu

et al. 2020

Remote Sensing

View full text Add to dashboard Cite

Low-rank tensors have received more attention in hyperspectral image (HSI) recovery. Minimizing the tensor nuclear norm, as a low-rank approximation method, often leads to modeling bias. To achieve an unbiased approximation and improve the robustness, this paper develops a non-convex relaxation approach for low-rank tensor approximation. Firstly, a non-convex approximation of tensor nuclear norm (NCTNN) is introduced to the low-rank tensor completion. Secondly, a non-convex tensor robust principal component analysis (NCTRPCA) method is proposed, which aims at exactly recovering a low-rank tensor corrupted by mixed-noise. The two proposed models are solved efficiently by the alternating direction method of multipliers (ADMM). Three HSI datasets are employed to exhibit the superiority of the proposed model over the low rank penalization method in terms of accuracy and robustness.

show abstract

“…However, such X is meaningless because it ignores the inner structure and correlation of the data. The most common way is to constrain X with rank or nuclear norm [22,23]. However, it introduces some hyperparameters, e.g., the upper limit for rank or norm.…”

Section: Problem Descriptionmentioning

confidence: 99%

Nonparametric Tensor Completion Based on Gradient Descent and Nonconvex Penalty

Xiong

2019

Symmetry

View full text Add to dashboard Cite

Existing tensor completion methods all require some hyperparameters. However, these hyperparameters determine the performance of each method, and it is difficult to tune them. In this paper, we propose a novel nonparametric tensor completion method, which formulates tensor completion as an unconstrained optimization problem and designs an efficient iterative method to solve it. In each iteration, we not only calculate the missing entries by the aid of data correlation, but consider the low-rank of tensor and the convergence speed of iteration. Our iteration is based on the gradient descent method, and approximates the gradient descent direction with tensor matricization and singular value decomposition. Considering the symmetry of every dimension of a tensor, the optimal unfolding direction in each iteration may be different. So we select the optimal unfolding direction by scaled latent nuclear norm in each iteration. Moreover, we design formula for the iteration step-size based on the nonconvex penalty. During the iterative process, we store the tensor in sparsity and adopt the power method to compute the maximum singular value quickly. The experiments of image inpainting and link prediction show that our method is competitive with six state-of-the-art methods.which is similar to Tucker decomposition. In the second approach, Nuclear Norm Minimization (NNM) is often used to replace RM because RM is NP-hard [14]. Reference [15] directly minimized the tensor nuclear norm for tensor completion. Reference [16] proposed a dual frame for low-rank tensor completion via nuclear norm constraints. Since high-order tensors represent a higher dimensional space, some works [17,18] used the Riemannian manifold for tensor completion, which is still closely linked to RM. In addition, some works [19,20] converted the tensor into matrices and realized tensor completion by means of matrix completion, but they ignored the inner structure and correlation of the data.The aforementioned methods of tensor completion all require some hyperparameters, such as the upper bound of the rank in the low-rank constraint and the penalty coefficient for norms. However, the selection of these hyperparameters not only consumes a substantial amount of time but also determines the performance of the methods. To address this issue, we propose a novel Nonparametric Tensor Completion (NTC) method based on gradient descent and nonconvex penalty. We use gradient descent to solve the optimization problem of tensor completion and build a gradient tensor with tensor matricizations and Singular Value Decomposition (SVD). We select the optimal direction based on the scaled latent nuclear norm in each iteration. The step-size in gradient descent is regarded as a penalty parameter for the singular value, and we design a nonconvex penalty for it. Furthermore, during the iterative process, we store the tensor in sparsity and adopt the power method to compute the maximum singular value quickly. Experiments of image inpainting and link prediction show that our metho...

show abstract

A non-convex tensor rank approximation for tensor completion

Cited by 88 publications

References 46 publications

Spatially Regularized Low Rank Tensor Optimization for Visual Data Completion

Spatially Regularized Low Rank Tensor Optimization for Visual Data Completion

Hyperspectral Image Recovery Using Non-Convex Low-Rank Tensor Approximation

Nonparametric Tensor Completion Based on Gradient Descent and Nonconvex Penalty

Contact Info

Product

Resources

About