mlsanityData to 14 Oct 2026

Accelerating Large-Scale Regularized High-Order Tensor Recovery

arXiv 2506.09594 ↗First posted 11 Jun 2025cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale high-order tensor data. To alleviate these issue, assisted by the Krylov subspace iteration, block Lanczos bidiagonalization process, and random projection strategies, this article first devises two fast and accurate randomized algorithms for low-rank tensor approximation (LRTA) problem. Theoretical bounds on the accuracy of the approximation error estimate are established. Next, we develop a novel generalized nonconvex modeling framework tailored to large-scale tensor recovery, in which a new regularization paradigm is exploited to achieve insightful prior representation for large-scale tensors. On the basis of the above, we further investigate new unified nonconvex models and efficient optimization algorithms, respectively, for several typical high-order tensor recovery tasks in unquantized and quantized situations. To render the proposed algorithms practical and efficient for large-scale tensor data, the proposed randomized LRTA schemes are integrated into their central and time-intensive computations. Finally, we conduct extensive experiments on various large-scale tensors, whose results demonstrate the practicability, effectiveness and superiority of the proposed method in comparison with some state-of-the-art approaches.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 40 of its 124 references that are in the map. First posted on arXiv 11 Jun 2025.

Builds on

40 of 124 references.

References · 40

  1. 2016Tensor Ring Decompositioncited by 127
  2. 2018Tensor Robust Principal Component Analysis with A New Tensor Nuclear Normcited by 112
  3. 2018Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clusteringcited by 94
  4. 2014Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determinationcited by 65
  5. 2015Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decompositioncited by 64
  6. 2016Efficient tensor completion for color image and video recovery: Low-rank tensor traincited by 61
  7. 2021Tensor Methods in Computer Vision and Deep Learningcited by 52
  8. 2019Bayesian Temporal Factorization for Multidimensional Time Series Predictioncited by 47
  9. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 46
  10. 2020Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restorationcited by 43
  11. 2023Guaranteed Tensor Recovery Fused Low-rankness and Smoothnesscited by 41
  12. 2020An Optimal Statistical and Computational Framework for Generalized Tensor Estimationcited by 39
28 more
  1. 2016Practical sketching algorithms for low-rank matrix approximationcited by 38
  2. 2013Robust Low-rank Tensor Recovery: Models and Algorithmscited by 34
  3. 2021Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurementscited by 28
  4. 2013A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problemscited by 25
  5. 2021Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimizationcited by 24
  6. 2015Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Normcited by 23
  7. 2014Bayesian Robust Tensor Factorization for Incomplete Multiway Datacited by 22
  8. 2018Tensor N-tubal rank and its convex relaxation for low-rank tensor recoverycited by 19
  9. 2016Low-tubal-rank Tensor Completion using Alternating Minimizationcited by 18
  10. 2021Provable Tensor-Train Format Tensor Completion by Riemannian Optimizationcited by 17
  11. 2019Low-Rank Tucker Approximation of a Tensor From Streaming Datacited by 15
  12. 2023Machine learning with tree tensor networks, CP rank constraints, and tensor dropoutcited by 15
  13. 2024Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimationcited by 15
  14. 2024Revisiting Nonlocal Self-Similarity from Continuous Representationcited by 14
  15. 2018Learning tensors from partial binary measurementscited by 13
  16. 2022High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantizationcited by 13
  17. 2019Block-Randomized Stochastic Proximal Gradient for Low-Rank Tensor Factorizationcited by 12
  18. 2019Tensor-Ring Nuclear Norm Minimization and Application for Visual Data Completioncited by 12
  19. 2017Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizerscited by 10
  20. 2020Streaming Coresets for Symmetric Tensor Factorizationcited by 9
  21. 2024Guaranteed Nonconvex Factorization Approach for Tensor Train Recoverycited by 8
  22. 2022Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Functioncited by 7
  23. 2024Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descentcited by 7
  24. 2020Robust Low-tubal-rank Tensor Completion based on Tensor Factorization and Maximum Correntopy Criterioncited by 6
  25. 2021Fully-Connected Tensor Network Decomposition for Robust Tensor Completion Problemcited by 5
  26. 2023On the Unreasonable Effectiveness of Single Vector Krylov Methods for Low-Rank Approximationcited by 4
  27. 2023Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizerscited by 3
  28. 2019An improved analysis and unified perspective on deterministic and randomized low rank matrix approximationscited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2026Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computation
  2. 2026EinSort: Sorting is All We Need for Tensorizing LLM
  3. 2025Score-Based Model for Low-Rank Tensor Recovery
  4. 2022Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction
  5. 2021Multi-Tensor Network Representation for High-Order Tensor Completion
  6. 2025Efficient Tensor Completion Algorithms for Highly Oscillatory Operators
  7. 2026Tucker Diffusion Model for High-dimensional Tensor Generation
  8. 2026High-Resolution Tensor-Network Fourier Methods for Exponentially Compressed Non-Gaussian Aggregate Distributions