T-product based \(\ell_1\)-norm tensor principal component analysis and a finite-step convergence algorithm

DOI10.1016/j.aml.2024.109318MaRDI QIDQ6656490

Yuning Yang, Xianpeng Mao

Publication date: 3 January 2025

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

tensorprincipal component analysisdimensionality reduction\(\ell_1\)-normt-product

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Nonlinear programming (90C30) Multilinear algebra, tensor calculus (15A69)

Cites Work

• Factorization strategies for third-order tensors
• T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming
• Facial Recognition Using Tensor-Tensor Decompositions
• Efficient L1-Norm Principal-Component Analysis via Bit Flipping
• L1-Norm Principal-Component Analysis of Complex Data
• Conditional Gradient Algorithmsfor Rank-One Matrix Approximations with a Sparsity Constraint
• Reduced-Rank L1-Norm Principal-Component Analysis With Performance Guarantees
• Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging
• Linear Convergence of a Proximal Alternating Minimization Method with Extrapolation for \(\boldsymbol{\ell_1}\) -Norm Principal Component Analysis
• Perturbation analysis on T-eigenvalues of third-order tensors
• Coseparable nonnegative tensor factorization with t-CUR decomposition

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