# Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentation

arXiv: https://arxiv.org/abs/2109.05736 · HTML: https://mlsanity.com/paper/2109.05736/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 79 references that are in the map.
- First posted on arXiv 13 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration](https://mlsanity.com/paper/1709.00192/) (2017)
- [Multi-View Spectral Clustering Tailored Tensor Low-Rank Representation](https://mlsanity.com/paper/2004.14705/) (2020)
- [Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains](https://mlsanity.com/paper/1804.06128/) (2018)
- [A dual framework for low-rank tensor completion](https://mlsanity.com/paper/1712.01193/) (2017)
- [Matrix Product State for Feature Extraction of Higher-Order Tensors](https://mlsanity.com/paper/1503.00516/) (2015)
- [Concatenated image completion via tensor augmentation and completion](https://mlsanity.com/paper/1607.03967/) (2016)

## Built on by (most cited first, 8 of 8)

- [Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descent](https://mlsanity.com/paper/2401.11940/) (2024)
- [When Can We Solve the Weighted Low Rank Approximation Problem in Truly Subquadratic Time?](https://mlsanity.com/paper/2502.16912/) (2025)
- [Bayesian Robust Tensor Ring Model for Incomplete Multiway Data](https://mlsanity.com/paper/2202.13321/) (2022)
- [Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization](https://mlsanity.com/paper/2506.22134/) (2025)
- [Scalable and Robust Tensor Ring Decomposition for Large-scale Data](https://mlsanity.com/paper/2305.09044/) (2023)
- [Quaternion tensor left ring decomposition and application for color image inpainting](https://mlsanity.com/paper/2307.10620/) (2023)
- [Hyperspectral Image Recovery Constrained by Multi-Granularity Non-Local Self-Similarity Priors](https://mlsanity.com/paper/2508.01435/) (2025)
- [Tensor Decomposition Structure Search Framework from an Interaction Perspective](https://mlsanity.com/paper/2603.02720/) (2026)

## Abstract (arXiv)

In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor completion methods using TT decomposition have two obvious drawbacks. One is that they only consider mode weights according to the degree of mode balance, even though some elements are recovered better in an unbalanced mode. The other is that serious blocking artifacts appear when the missing element rate is relatively large. To remedy such two issues, in this work, we propose a novel tensor completion approach via the element-wise weighted technique. Accordingly, a novel formulation for tensor completion and an effective optimization algorithm, called as tensor completion by parallel weighted matrix factorization via tensor train (TWMac-TT), is proposed. In addition, we specifically consider the recovery quality of edge elements from adjacent blocks. Different from traditional reshaping and ket augmentation, we utilize a new tensor augmentation technique called overlapping ket augmentation, which can further avoid blocking artifacts. We then conduct extensive performance evaluations on synthetic data and several real image data sets. Our experimental results demonstrate that the proposed algorithm TWMac-TT outperforms several other competing tensor completion methods.