# Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion

arXiv: https://arxiv.org/abs/1809.02288 · HTML: https://mlsanity.com/paper/1809.02288/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2018.

## Built on by (most cited first, 30 of 42)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restoration](https://mlsanity.com/paper/2303.06682/) (2023)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [Revisiting Nonlocal Self-Similarity from Continuous Representation](https://mlsanity.com/paper/2401.00708/) (2024)
- [Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion](https://mlsanity.com/paper/2110.08774/) (2021)
- [Permutation Search of Tensor Network Structures via Local Sampling](https://mlsanity.com/paper/2206.06597/) (2022)
- [SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective](https://mlsanity.com/paper/2305.14912/) (2023)
- [Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery](https://mlsanity.com/paper/2401.02592/) (2024)
- [Nonlocal Patch-Based Fully-Connected Tensor Network Decomposition for Remote Sensing Image Inpainting](https://mlsanity.com/paper/2109.05889/) (2021)
- [Interaction Decompositions for Tensor Network Regression](https://mlsanity.com/paper/2208.06029/) (2022)
- [HADAR-Based Thermal Infrared Hyperspectral Image Restoration](https://mlsanity.com/paper/2605.13664/) (2026)
- [Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data](https://mlsanity.com/paper/2106.10422/) (2021)
- [Patch Tracking-based Streaming Tensor Ring Completion for Visual Data Recovery](https://mlsanity.com/paper/2105.14620/) (2021)
- [Multi-Tensor Network Representation for High-Order Tensor Completion](https://mlsanity.com/paper/2109.04022/) (2021)
- [Bayesian Robust Tensor Ring Model for Incomplete Multiway Data](https://mlsanity.com/paper/2202.13321/) (2022)
- [A high-order tensor completion algorithm based on Fully-Connected Tensor Network weighted optimization](https://mlsanity.com/paper/2204.01732/) (2022)
- [Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysis](https://mlsanity.com/paper/2412.03321/) (2024)
- [Hyperspectral Anomaly Detection Fused Unified Nonconvex Tensor Ring Factors Regularization](https://mlsanity.com/paper/2505.17881/) (2025)
- [Lower and Upper Bounds on the VC-Dimension of Tensor Network Models](https://mlsanity.com/paper/2106.11827/) (2021)
- [Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularization](https://mlsanity.com/paper/2205.03059/) (2022)
- [Non-convex approaches for low-rank tensor completion under tubal sampling](https://mlsanity.com/paper/2303.12721/) (2023)
- [Image Reconstruction using Superpixel Clustering and Tensor Completion](https://mlsanity.com/paper/2305.09564/) (2023)
- [Multi-Dictionary Tensor Decomposition](https://mlsanity.com/paper/2309.09717/) (2023)
- [DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recovery](https://mlsanity.com/paper/2407.05267/) (2024)
- [Generalized Least Squares Kernelized Tensor Factorization](https://mlsanity.com/paper/2412.07041/) (2024)
- [Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2511.14270/) (2025)
- [Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2603.01034/) (2026)

## Abstract (arXiv)

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure of the TR latent space, we propose a novel tensor completion method which is robust to model selection. In contrast to imposing the low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in the optimization step using singular value decomposition (SVD) being performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm is shown to effectively alleviate the burden of TR-rank selection, thereby greatly reducing the computational cost. The extensive experimental results on both synthetic and real-world data demonstrate the superior performance and efficiency of the proposed approach against the state-of-the-art algorithms.