Robust recovery of multiple subspaces by geometric \(l_{p}\) minimization

DOI10.1214/11-AOS914zbMath1232.62097arXiv1104.3770MaRDI QIDQ661178

Teng Zhang, Gilad Lerman

Publication date: 21 February 2012

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.3770

zbMATH Keywords

robustnessclusteringhigh-dimensional datadetectiongeometric probabilityhybrid linear modelingoptimization of Grassmannians

Mathematics Subject Classification ID

Multivariate analysis (62H99) Nonparametric robustness (62G35) Classification and discrimination; cluster analysis (statistical aspects) (62H30)

Related Items (23)

Applied harmonic analysis and sparse approximation. Abstracts from the workshop held June 10--16, 2012. ⋮ Inference and mixture modeling with the elliptical Gamma distribution ⋮ Learning Subspaces of Different Dimensions ⋮ A geometric analysis of subspace clustering with outliers ⋮ Hybrid linear modeling via local best-fit flats ⋮ A new approach to two-view motion segmentation using global dimension minimization ⋮ Sampling-based dimension reduction for subspace approximation with outliers ⋮ Numerical Algorithms on the Affine Grassmannian ⋮ \(l_p\)-recovery of the most significant subspace among multiple subspaces with outliers ⋮ The equivalence between principal component analysis and nearest flat in the least square sense ⋮ Local Linear Regression on Manifolds and Its Geometric Interpretation ⋮ Robust subspace clustering ⋮ Reduced row echelon form and non-linear approximation for subspace segmentation and high-dimensional data clustering ⋮ Testing the manifold hypothesis ⋮ On the robust PCA and Weiszfeld's algorithm ⋮ Sheaf-theoretic stratification learning from geometric and topological perspectives ⋮ The shape of data and probability measures ⋮ The Grassmannian of affine subspaces ⋮ Unnamed Item ⋮ Schubert Varieties and Distances between Subspaces of Different Dimensions ⋮ Topological inference of manifolds with boundary ⋮ A Well-Tempered Landscape for Non-convex Robust Subspace Recovery ⋮ Robust computation of linear models by convex relaxation

Cites Work

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• \(l_p\)-recovery of the most significant subspace among multiple subspaces with outliers
• Foundations of a multi-way spectral clustering framework for hybrid linear modeling
• Optimal non-linear models for sparsity and sampling
• Strong consistency of k-means clustering
• A central limit theorem for k-means clustering
• Nearest \(q\)-flat to \(m\) points
• \(k\)-plane clustering
• Hybrid linear modeling via local best-fit flats
• Spectral clustering based on local linear approximations
• Robust principal component analysis?
• Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data
• On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel-PCA
• Geometric motion segmentation and model selection

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