# Bayesian Robust Tensor Ring Model for Incomplete Multiway Data

arXiv: https://arxiv.org/abs/2202.13321 · HTML: https://mlsanity.com/paper/2202.13321/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 27 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [A Comprehensive Survey of Scene Graphs: Generation and Application](https://mlsanity.com/paper/2104.01111/) (2021)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration](https://mlsanity.com/paper/2010.12921/) (2020)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations](https://mlsanity.com/paper/2103.06842/) (2021)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm](https://mlsanity.com/paper/1712.05870/) (2017)
- [Tucker decomposition-based Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2011.07751/) (2020)
- [Efficient Nonnegative Tucker Decompositions: Algorithms and Uniqueness](https://mlsanity.com/paper/1404.4412/) (2014)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [Tensor-Ring Nuclear Norm Minimization and Application for Visual Data Completion](https://mlsanity.com/paper/1903.08888/) (2019)
- [Provable Tensor Ring Completion](https://mlsanity.com/paper/1903.03315/) (2019)
- [Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentation](https://mlsanity.com/paper/2109.05736/) (2021)
- [Efficient Tensor Robust PCA under Hybrid Model of Tucker and Tensor Train](https://mlsanity.com/paper/2112.10771/) (2021)

## Built on by (most cited first, 2 of 2)

- [Latent Matrices for Tensor Network Decomposition and to Tensor Completion](https://mlsanity.com/paper/2210.03392/) (2022)
- [A PID-Controlled Tensor Wheel Decomposition Model for Dynamic Link Prediction](https://mlsanity.com/paper/2505.14211/) (2025)

## Abstract (arXiv)

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observation with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the existing methods either require a pre-assigned TR rank or aggressively pursue the minimum TR rank, thereby often leading to biased solutions in the presence of noise. In this paper, a Bayesian robust tensor ring decomposition (BRTR) method is proposed to give more accurate solutions to the RTC problem, which can avoid exquisite selection of the TR rank and penalty parameters. A variational Bayesian (VB) algorithm is developed to infer the probability distribution of posteriors. During the learning process, BRTR can prune off slices of core tensor with marginal components, resulting in automatic TR rank detection. Extensive experiments show that BRTR can achieve significantly improved performance than other state-of-the-art methods.