A nonconvex formulation for low rank subspace clustering: algorithms and convergence analysis
type: Item
instance of: scholarly article
title: A nonconvex formulation for low rank subspace clustering: algorithms and convergence analysis
zbMATH Open document ID: 1404.90126
author: Hao Jiang
author: Daniel P. Robinson
author: Chong You
author: René Vidal
published in: Computational Optimization and Applications
publication date: 2018-06-13T00:00:00Z
review text: The authors obtain a low rank subspace clustering method based on non-convex modeling in order to give a solution to the problem of subspace clustering with data that is potentially corrupted by both dense noise and sparse gross errors. Refined smoothness properties of the spectral function are derived and used to establish the convergence of the alternating direction method of multipliers proposed for solving the non-convex problem. It is proved that the iterates are uniformly bounded and all limit points verify the first-order optimality conditions. Numerical experiments prove the efficiency of the technique. They process real data from face and digit clustering and motion segmentation.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6887475
zbMATH Keywords: ADMM
zbMATH Keywords: nonconvex
zbMATH Keywords: subspace clustering
describes a project that uses: OpenCV
MaRDI profile type: Publication
full work available at URL: s10589-018-0002-6
OpenAlex ID: W2795293001
cites work: Operator-Lipschitz estimates for the singular value functional calculus
cites work: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
cites work: A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
cites work: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
cites work: Minimization of non-smooth, non-convex functionals by iterative thresholding
cites work: Robust principal component analysis?
cites work: The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent
cites work: Trust Region Methods
cites work: Q3466913
cites work: Robust subspace clustering
cites work: A dual algorithm for the solution of nonlinear variational problems via finite element approximation
cites work: Q4144736
cites work: Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems
cites work: Nonsmooth analysis of singular values. I: Theory
cites work: Splitting Algorithms for the Sum of Two Nonlinear Operators
cites work: A geometric analysis of subspace clustering with outliers
cites work: Q3161693
cites work: Generalized principal component analysis
cites work: Relations Among Some Low-Rank Subspace Recovery Models
DOI: 10.1007/S10589-018-0002-6
description: scientific article; zbMATH DE number 6887475