Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics

1977/01/01 by Joseph B. Kruskal · 68 citations
Mathematics · Engineering · Computer Science · #Tensor decomposition and applications #Sparse and Compressive Sensing Techniques #Matrix Theory and Algorithms

paper · doi:10.1016/0024-3795(77)90069-6

Cited by

• Tensor Decompositions and Applications
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• Estimation under group actions: Recovering orbits from invariants
• Identifiability of restricted latent class models with binary responses
• Multiscale Methods for Discretized Continuous Optimization: Convergence and Cost Analysis
• Tensor-Based Dynamic Channel Estimation for mmWave Movable Antenna MIMO Systems
• Integrated Channel Estimation and Sensing for Near-Field ELAA Systems via Low-Rank Tensor Decomposition
• Uniqueness of Tensor Decompositions with Applications to Polynomial Identifiability
• Hidden Markov Model Identifiability via Tensors
• Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Data
• Two classes of minimal generic fundamental invariants for tensors
• Discussion of "The Blessings of Multiple Causes" by Wang and Blei
• Doubly Decomposing Nonparametric Tensor Regression
• Beyond ICA: Identifiability by Symmetry Breaking
• Efficient Tensor Decomposition
• Identification of Multivariate Measurement Error Models
• Comparing Two Proxy Methods for Causal Identification
• Symmetric tensors and symmetric tensor rank
• A Fully Probabilistic Tensor Network for Regularized Volterra System Identification
• A Generalized Additive Partial-Mastery Cognitive Diagnosis Model
• Computation of Generalized Inverses of Tensors via t-Product
• Fault Oblivious Eigenvalue Solver
• Link Prediction on N-ary Relational Facts: A Graph-based Approach
• A Novel Block-Alternating Iterative Algorithm for Retrieving Top-k Elements from Factorized Tensors
• Channel Estimation for Millimeter Wave Multiuser MIMO Systems via PARAFAC Decomposition
• Consensus-based In-Network Computation of the PARAFAC Decomposition
• Using spatial modeling to address covariate measurement error
• No-rank Tensor Decomposition Using Metric Learning
• Tensor decomposition beyond uniqueness, with an application to the minrank problem
• On partial and generic uniqueness of block term tensor decompositions
• An Axiomatic Approach to Tensor Rank Functions
• Theoretical Grounding for Estimation in Conditional Independence Multivariate Finite Mixture Models
• When Does Non-Orthogonal Tensor Decomposition Have No Spurious Local\n Minima?
• On the identifiability of binary Segre products
• Tensor Decomposition for Signal Processing and Machine Learning
• Guaranteed Simultaneous Asymmetric Tensor Decomposition via Orthogonalized Alternating Least Squares
• Low-Rank Tensor Decomposition-Aided Channel Estimation for Millimeter Wave MIMO-OFDM Systems
• Kullback-Leibler Principal Component for Tensors is not NP-hard
• Hermitian Tensor Decompositions
• Bilinear Complexity of 3-Tensors Linked to Coding Theory
• Multi-subspace power method for decomposing partially symmetric tensors
• Hierarchical multilinear models for multiway data
• Data Understanding Survey: Pursuing Improved Dataset Characterization Via Tensor-based Methods
• On The Identifiability of Mixture Models from Grouped Samples
• A Spatio-temporal CP decomposition analysis of New England region in the US
• Best approximation on semi-algebraic sets and k-border rank\n approximation of symmetric tensors
• Towards Sampling Data Structures for Tensor Products in Turnstile Streams
• Guaranteed Noisy CP Tensor Recovery via Riemannian Optimization on the Segre Manifold
• Score Function Features for Discriminative Learning: Matrix and Tensor Framework
• Generalized Nonnegative Structured Kruskal Tensor Regression
• The multilinear forms Cayley graph and the eigenvalue method for tensor codes
• Nonparametric Estimation of Multi-View Latent Variable Models
• Streaming Coresets for Symmetric Tensor Factorization
• Improved Bounds on Restricted Isometry Constants for Gaussian Matrices
• Optimal estimation of high-dimensional location Gaussian mixtures
• Low Rank Approximation of Tensors via Sparse Optimization
• Provable Sparse Tensor Decomposition
• A Statistical Test for Comparing the Linkage and Admixture Model Based on Central Limit Theorems
• Minimal Realization Problems for Hidden Markov Models
• Coupled tensor models for probability mass function estimation: Part II, Uniqueness of the model
• On global convergence of alternating least squares for tensor approximation
• Convex relaxation approaches for strictly correlated density functional theory
• Low-rank Matrix Recovery With Unknown Correspondence
• Identifiability of Large Phylogenetic Mixtures for Many Phylogenetic Model Structures
• About Notations in Multiway Array Processing
• Partial Identifiability of Restricted Latent Class Models
• Spectral Learning for Supervised Topic Models
• Compressed Factorization: Fast and Accurate Low-Rank Factorization of Compressively-Sensed Data