Computing non-negative tensor factorizations

DOI10.1080/10556780801996244zbMath1158.65321OpenAlexW2038647687WikidataQ114099392 ScholiaQ114099392MaRDI QIDQ5503698

Kathrin Hatz, Michael P. Friedlander

Publication date: 16 January 2009

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556780801996244

zbMATH Keywords

regularizationtensorssparse solutionsnon-negative tensor factorizationalternating least-squaresblock Gauss-Seidel\(N\)-dimensional arraysnon-negative least-squares

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Quadratic programming (90C20) Multilinear algebra, tensor calculus (15A69) Packaged methods for numerical algorithms (65Y15)

Related Items (16)

Computational experience with numerical methods for nonnegative least-squares problems ⋮ A very brief introduction to nonnegative tensors from the geometric viewpoint ⋮ Randomized algorithms for the approximations of Tucker and the tensor train decompositions ⋮ A reduced Newton method for constrained linear least-squares problems ⋮ Variational auto-encoder based Bayesian Poisson tensor factorization for sparse and imbalanced count data ⋮ The Computation of Low Multilinear Rank Approximations of Tensors via Power Scheme and Random Projection ⋮ A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search. ⋮ Randomized algorithms for the low multilinear rank approximations of tensors ⋮ Orthogonal Nonnegative Tucker Decomposition ⋮ Factorization strategies for third-order tensors ⋮ Image representation using Laplacian regularized nonnegative tensor factorization ⋮ Best Nonnegative Rank-One Approximations of Tensors ⋮ Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework ⋮ Tensors of nonnegative rank two ⋮ An AO-ADMM Approach to Constraining PARAFAC2 on All Modes ⋮ Alternating proximal gradient method for sparse nonnegative Tucker decomposition

Uses Software

• Matlab
• BCLS

Cites Work

• On the convergence of the coordinate descent method for convex differentiable minimization
• Atomic Decomposition by Basis Pursuit
• Positive tensor factorization
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Algorithm 862
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Trust Region Methods
• A Multilinear Singular Value Decomposition
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Learning the parts of objects by non-negative matrix factorization
• Projected Gradient Methods for Nonnegative Matrix Factorization
• Stable signal recovery from incomplete and inaccurate measurements
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