Parameter selection for nonnegative $l_1$ matrix/tensor sparse decomposition

DOI10.1016/j.orl.2015.06.005zbMath1408.15010OpenAlexW609313498MaRDI QIDQ1785395

Wanquan Liu, Louis Caccetta, Guanglu Zhou, Y. J. Wang

Publication date: 28 September 2018

Published in: Operations Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.orl.2015.06.005

zbMATH Keywords

global optimal solutionregularization parameterzero solutionsparse decompositionthreshold bound

Mathematics Subject Classification ID

Factorization of matrices (15A23) Applications of mathematical programming (90C90) Quadratic programming (90C20) Multilinear algebra, tensor calculus (15A69) Linear equations (linear algebraic aspects) (15A06)

Related Items (16)

Smoothing approximation to the lower order exact penalty function for inequality constrained optimization ⋮ Modified hybrid decomposition of the augmented Lagrangian method with larger step size for three-block separable convex programming ⋮ Further results on sum-of-squares tensors ⋮ Alternating proximal penalization algorithm for the modified multiple-sets split feasibility problems ⋮ A Geršgorin-type eigenvalue localization set with \(n\) parameters for stochastic matrices ⋮ An accelerated proximal augmented Lagrangian method and its application in compressive sensing ⋮ A sparse rank-1 approximation algorithm for high-order tensors ⋮ On phaseless compressed sensing with partially known support ⋮ Some Ostrowski-type bound estimations of spectral radius for weakly irreducible nonnegative tensors ⋮ An Inexact Projected Gradient Method for Sparsity-Constrained Quadratic Measurements Regression ⋮ Proximal ADMM with larger step size for two-block separable convex programming and its application to the correlation matrices calibrating problems ⋮ An alternative extragradient projection method for quasi-equilibrium problems ⋮ An SDP method for copositivity of partially symmetric tensors ⋮ On computing minimal \(H\)-eigenvalue of sign-structured tensors ⋮ Solution structures of tensor complementarity problem ⋮ On copositiveness identification of partially symmetric rectangular tensors

Uses Software

• PMA

Cites Work

• Unnamed Item
• A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
• Breakdown of equivalence between the minimal \(\ell^1\)-norm solution and the sparsest solution
• Biclustering in data mining
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• For most large underdetermined systems of linear equations the minimal 𝓁₁‐norm solution is also the sparsest solution

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