mlsanityData to 7 Oct 2026

Efficient Low Rank Tensor Ring Completion

arXiv 1707.08184 ↗First posted 23 Jul 2017cs.LG cs.IT math.ITcited by 45

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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.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Jul 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 9; 2023: 16; 2024: 1; 2025: 5; 2026: 3.

45 papers.

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  1. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 45
  2. 2023Guaranteed Tensor Recovery Fused Low-rankness and Smoothnesscited by 41
  3. 2021Convolutional Neural Network Compression through Generalized Kronecker Product Decompositioncited by 14
  4. 2022Generative modeling via tensor train sketchingcited by 13
  5. 2022Noisy Tensor Completion via Low-rank Tensor Ringcited by 13
  6. 2022Permutation Search of Tensor Network Structures via Local Samplingcited by 13
  7. 2023Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluationscited by 12
  8. 2021Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentationcited by 8
  9. 2023Generative Modeling via Hierarchical Tensor Sketchingcited by 8
  10. 2021More Efficient Sampling for Tensor Decomposition With Worst-Case Guaranteescited by 7
  11. 2023Multi-view MERA Subspace Clusteringcited by 7
  12. 2023Adaptively Topological Tensor Network for Multi-view Subspace Clusteringcited by 4
33 more
  1. 2021Partially Observed Exchangeable Modelingcited by 3
  2. 2021Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Datacited by 3
  3. 2021Semi-tensor Product-based TensorDecomposition for Neural Network Compressioncited by 3
  4. 2022Classical Simulation of Variational Quantum Classifiers using Tensor Ringscited by 3
  5. 2022How to Train Unstable Looped Tensor Networkcited by 3
  6. 2023To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completioncited by 3
  7. 2021Patch Tracking-based Streaming Tensor Ring Completion for Visual Data Recoverycited by 2
  8. 2021Multi-Tensor Network Representation for High-Order Tensor Completioncited by 2
  9. 2022Bayesian Robust Tensor Ring Model for Incomplete Multiway Datacited by 2
  10. 2022A high-order tensor completion algorithm based on Fully-Connected Tensor Network weighted optimizationcited by 2
  11. 2023TERM Model: Tensor Ring Mixture Model for Density Estimationcited by 2
  12. 2024Scalable Bayesian Tensor Ring Factorization for Multiway Data Analysiscited by 2
  13. 2021Lower and Upper Bounds on the VC-Dimension of Tensor Network Modelscited by 1
  14. 2021Learning Circular Hidden Quantum Markov Models: A Tensor Network Approachcited by 1
  15. 2023A generalizable framework for low-rank tensor completion with numerical priorscited by 1
  16. 2023Image Reconstruction using Superpixel Clustering and Tensor Completioncited by 1
  17. 2026Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recoverycited by 1
  18. 2021Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximationcited by 0
  19. 2022SeKron: A Decomposition Method Supporting Many Factorization Structurescited by 0
  20. 2023Scalable and Robust Tensor Ring Decomposition for Large-scale Datacited by 0
  21. 2023Optical Coherence Tomography Image Enhancement via Block Hankelization and Low Rank Tensor Network Approximationcited by 0
  22. 2023Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimizationcited by 0
  23. 2023Tensor Completion via Leverage Sampling and Tensor QR Decomposition for Network Latency Estimationcited by 0
  24. 2023Quaternion tensor left ring decomposition and application for color image inpaintingcited by 0
  25. 2023Hyperspectral Image Fusion via Logarithmic Low-rank Tensor Ring Decompositioncited by 0
  26. 2023Low-Multi-Rank High-Order Bayesian Robust Tensor Factorizationcited by 0
  27. 2025Score-Based Model for Low-Rank Tensor Recoverycited by 0
  28. 2025Normalized Iterative Hard Thresholding for Tensor Recoverycited by 0
  29. 2025Superpixel-informed Continuous Low-Rank Tensor Representation for Multi-Dimensional Data Recoverycited by 0
  30. 2025Efficient Tensor Completion Algorithms for Highly Oscillatory Operatorscited by 0
  31. 2025An Interdisciplinary and Cross-Task Review on Missing Data Imputationcited by 0
  32. 2026Neural Operator-Grounded Continuous Tensor Function Representation and Its Applicationscited by 0
  33. 2026Tensor Decomposition Structure Search Framework from an Interaction Perspectivecited by 0