# Efficient Low Rank Tensor Ring Completion

arXiv: https://arxiv.org/abs/1707.08184 · HTML: https://mlsanity.com/paper/1707.08184/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2017.

## Built on by (most cited first, 30 of 45)

- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Guaranteed Tensor Recovery Fused Low-rankness and Smoothness](https://mlsanity.com/paper/2302.02155/) (2023)
- [Convolutional Neural Network Compression through Generalized Kronecker Product Decomposition](https://mlsanity.com/paper/2109.14710/) (2021)
- [Generative modeling via tensor train sketching](https://mlsanity.com/paper/2202.11788/) (2022)
- [Noisy Tensor Completion via Low-rank Tensor Ring](https://mlsanity.com/paper/2203.08857/) (2022)
- [Permutation Search of Tensor Network Structures via Local Sampling](https://mlsanity.com/paper/2206.06597/) (2022)
- [Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluations](https://mlsanity.com/paper/2304.12875/) (2023)
- [Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentation](https://mlsanity.com/paper/2109.05736/) (2021)
- [Generative Modeling via Hierarchical Tensor Sketching](https://mlsanity.com/paper/2304.05305/) (2023)
- [More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees](https://mlsanity.com/paper/2110.07631/) (2021)
- [Multi-view MERA Subspace Clustering](https://mlsanity.com/paper/2305.09095/) (2023)
- [Adaptively Topological Tensor Network for Multi-view Subspace Clustering](https://mlsanity.com/paper/2305.00716/) (2023)
- [Partially Observed Exchangeable Modeling](https://mlsanity.com/paper/2102.06083/) (2021)
- [Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data](https://mlsanity.com/paper/2106.10422/) (2021)
- [Semi-tensor Product-based TensorDecomposition for Neural Network Compression](https://mlsanity.com/paper/2109.15200/) (2021)
- [Classical Simulation of Variational Quantum Classifiers using Tensor Rings](https://mlsanity.com/paper/2201.08878/) (2022)
- [How to Train Unstable Looped Tensor Network](https://mlsanity.com/paper/2203.02617/) (2022)
- [To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion](https://mlsanity.com/paper/2306.11123/) (2023)
- [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)
- [TERM Model: Tensor Ring Mixture Model for Density Estimation](https://mlsanity.com/paper/2312.08075/) (2023)
- [Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysis](https://mlsanity.com/paper/2412.03321/) (2024)
- [Lower and Upper Bounds on the VC-Dimension of Tensor Network Models](https://mlsanity.com/paper/2106.11827/) (2021)
- [Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach](https://mlsanity.com/paper/2111.01536/) (2021)
- [A generalizable framework for low-rank tensor completion with numerical priors](https://mlsanity.com/paper/2302.05881/) (2023)
- [Image Reconstruction using Superpixel Clustering and Tensor Completion](https://mlsanity.com/paper/2305.09564/) (2023)
- [Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2603.01034/) (2026)
- [Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximation](https://mlsanity.com/paper/2109.02314/) (2021)

## Abstract (arXiv)

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and analyze the computational complexity of the proposed algorithm. We numerically compare it with existing methods that employ a low rank tensor train approximation for data completion and show that our method outperforms the existing ones for a variety of real computer vision settings, and thus demonstrate the improved expressive power of tensor ring as compared to tensor train.