On the rotational invariant \(L_1\)-norm PCA

DOI10.1016/j.laa.2019.10.030OpenAlexW2984527396MaRDI QIDQ2174418

Max Nimmer, Sebastian Neumayer, Simon Setzer, Gabriele Drauschke

Publication date: 21 April 2020

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.03840

zbMATH Keywords

principal component analysisdimensionality reductionFrank-Wolfe algorithmconditional gradient algorithmoptimization on Grassmann manifoldsrobust subspace fitting

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Numerical optimization and variational techniques (65K10) Partial differential equations on manifolds; differential operators (58Jxx)

Related Items (4)

On the robust PCA and Weiszfeld's algorithm ⋮ Robust PCA via regularized \textsc{Reaper} with a matrix-free proximal algorithm ⋮ PCA reduced Gaussian mixture models with applications in superresolution ⋮ Parseval proximal neural networks

Uses Software

• FMS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Robust \(\ell_1\) approaches to computing the geometric median and principal and independent components
• Technical note: Directional derivatives in nonsmooth optimization
• A distribution-free M-estimator of multivariate scatter
• On gradients of functions definable in o-minimal structures
• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
• Two proposals for robust PCA using semidefinite programming
• Weiszfeld's method: old and new results
• Robust computation of linear models by convex relaxation
• Generalized power method for sparse principal component analysis
• Robust principal component analysis?
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming
• Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo
• The Geometry of Algorithms with Orthogonality Constraints
• Robust subspace recovery by Tyler's M-estimator
• A Well-Tempered Landscape for Non-convex Robust Subspace Recovery
• Conditional Gradient Algorithmsfor Rank-One Matrix Approximations with a Sparsity Constraint
• Fast, robust and non-convex subspace recovery
• Robust PCA via Outlier Pursuit
• A Majorize–Minimize Strategy for Subspace Optimization Applied to Image Restoration
• Robust Statistics
• On a Projected Weiszfeld Algorithm
• Robust Statistics
• Robust Statistics

This page was built for publication: On the rotational invariant \(L_1\)-norm PCA