Factorization strategies for third-order tensors

2010/10/26 by Misha E. Kilmer, Carla D. Martin · 1,338 citations
Computer Science · Mathematics · #Algebra over a field #Algorithm #Combinatorics #Factorization #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix multiplication #Multiplication (music) #Operator (biology) #Order (exchange) #Orthogonality #Pure mathematics #Rank (graph theory) #Representation (politics) #Tensor (intrinsic definition) #Tensor decomposition and applications #Tensor product #Wireless Communication Networks Research

paper · pdf · doi:10.1016/j.laa.2010.09.020

published in Linear Algebra and its Applications 435(3), 641-658 (Elsevier BV)

openalex publication_date 2010/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Cited by

• A JoLT for the KV Cache: Near-Lossless KV Cache Compression via Joint Tucker and JL-Residual Allocation for LLMs
• On limiting probability distributions of higher order Markov chains
• Image Denoising Using Global and Local Circulant Representation
• Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability
• Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform
• Efficient Low-Tubal-Rank Tensor Estimation via Alternating Preconditioned Gradient Descent
• Computation of Generalized Inverses of Tensors via t-Product
• iFCTN: an intra-block Fully-Connected Tensor Network Decomposition for Tensor Completion
• Gaussian Splatting-based Low-Rank Tensor Representation for Multi-Dimensional Image Recovery
• Tensor Kernel Recovery for Spatio-Temporal Hawkes Processes
• Regularized Kaczmarz Algorithms for Tensor Recovery
• An Interdisciplinary and Cross-Task Review on Missing Data Imputation
• Moore-Penrose inverse of quaternion tensors via M-product with applications in color image classification
• Tensor Q-Rank: New Data Dependent Definition of Tensor Rank
• RIP-based performance guarantee for low-tubal-rank tensor recovery
• Stable Tensor Neural Networks for Rapid Deep Learning
• A Study on Nonnegative Tubal Matrices
• Generalized T-product Tensor Bernstein Bounds
• Low-Rank High-Order Tensor Completion With Applications in Visual Data
• Tensor Restricted Isometry Property Analysis For a Large Class of Random Measurement Ensembles
• On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization
• Data Understanding Survey: Pursuing Improved Dataset Characterization Via Tensor-based Methods
• Multi-Slice Low-Rank Tensor Decomposition Based Multi-Atlas Segmentation: Application to Automatic Pathological Liver CT Segmentation
• Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers
• Novel Factorization Strategies for Higher Order Tensors: Implications for Compression and Recovery of Multi-linear Data
• Stochastic Gradient Descent for Incomplete Tensor Linear Systems
• Compact Multi-level-prior Tensor Representation for Hyperspectral Image Super-resolution
• Accelerating Large-Scale Regularized High-Order Tensor Recovery
• Randomized Kaczmarz for Tensor Linear Systems
• DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages
• A Ternary Non-Commutative Latent Factor Model for Scalable Three-Way Real Tensor Completion
• Higher Degree t-Hermitian Forms and Positivity-Preserving Contractions
• T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming
• Real-Time Network Traffic Forecasting with Missing Data: A Generative Model Approach
• Discrete cosine transform LSQR and GMRES methods for multidimensional ill-posed problems
• Morton Filters for Superior Template Protection for Iris Recognition
• Quantum tensor singular value decomposition with applications to recommendation systems
• On the tensor nuclear norm and the total variation regularization for image and video completion
• T-Jordan Canonical Form and T-Drazin Inverse based on the T-Product
• Superpixel-informed Continuous Low-Rank Tensor Representation for Multi-Dimensional Data Recovery
• Efficient Image Denoising Using Global and Local Circulant Representation
• A tensor-based dynamic mode decomposition based on the ⋆_\boldsymbolM-product
• Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
• Robust Low-tubal-rank Tensor Completion based on Tensor Factorization and Maximum Correntopy Criterion
• Tensor Dynamic Mode Decomposition
• An Image Noise Level Estimation Based on Tensor T-Product
• T-Singular Values and T-Sketching for Third Order Tensors
• On some tensor tubal-Krylov subspace methods via the T-product
• Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm
• Frequency-Weighted Robust Tensor Principal Component Analysis
• Tensor Sparse and Low-Rank based Submodule Clustering Method for Multi-way Data
• Denoising and Completion of 3D Data via Multidimensional Dictionary Learning
• T-Quadratic Forms and Spectral Analysis of T-Symmetric Tensors
• p-order Tensor Products with Invertible Linear Transforms
• Completion of the DrugMatrix Toxicogenomics Database using 3-Dimensional Tensors
• Riemannian Conjugate Gradient Descent Method for Third-Order Tensor Completion
• Tensor GMRES and Golub-Kahan Bidiagonalization methods via the Einstein product with applications to image and video processing
• Tensor extrapolation methods with applications
• On the computation of tensor functions under tensor-tensor multiplications with linear maps
• T-product Tensor Expander Chernoff Bound
• Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detection
• Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization
• T product Tensors Part I: Inequalities
• Low-rank Multi-view Clustering in Third-Order Tensor Space
• Tensor Completion via a Low-Rank Approximation Pursuit
• Tensor robust principal component analysis via the tensor nuclear over Frobenius norm
• Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion
• Demystifying Tubal Tensor Algebra
• Multi-Tensor Network Representation for High-Order Tensor Completion
• A Convergent Semi-Proximal Alternating Direction Method of Multipliers for Recovering Internet Traffics from Link Measurements
• On some tensor inequalities based on the t-product
• Matrices over a Hilbert space and their low-rank approximation
• Triple Decomposition and Tensor Recovery of Third Order Tensors
• Exact Tensor Completion from Sparsely Corrupted Observations via Convex Optimization
• High-order Graph Neural Networks with Common Neighbor Awareness for Link Prediction
• Exact matrix completion based on low rank Hankel structure in the Fourier domain
• Efficient iterative techniques for solving tensor problems with the T-product
• A higher-order LQ decomposition for separable covariance models
• Quasitubal Tensor Algebra Over Separable Hilbert Spaces
• Data-driven model order reduction for T-Product-Based dynamical systems
• Property Inheritance for Subtensors in Tensor Train Decompositions
• Randomized block Krylov method for approximation of truncated tensor SVD
• 3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction. [europepmc]
• Multi-energy CT reconstruction using tensor nonlocal similarity and spatial sparsity regularization. [europepmc]
• Color Image Restoration Using Sub-Image Based Low-Rank Tensor Completion. [europepmc]
• ITRPCA: a new model for computational drug repositioning based on improved tensor robust principal component analysis. [europepmc]
• BS-CP: Efficient streaming Bayesian tensor decomposition method via assumed density filtering. [europepmc]
• MULTIPAR: Supervised Irregular Tensor Factorization with Multi-task Learning for Computational Phenotyping. [europepmc]
• Collaborative representation based on enhanced tensor robust PCA for hyperspectral anomaly detection. [europepmc]
• Interpretable nonconvex submodule clustering algorithm using ℓr-induced tensor nuclear norm and ℓ2,p column sparse norm with global convergence guarantees. [europepmc]
• Network models for bridging denoising and identifying spatial domains of spatially resolved transcriptomics. [europepmc]