Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data

DOI10.1137/060655523zbMath1147.52010OpenAlexW2003361735MaRDI QIDQ3522875

Allen Y. Yang, Yi Ma, H. G. J. Derksen, Robert M. Fossum

Publication date: 4 September 2008

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/060655523

zbMATH Keywords

model selection Hilbert function subspace arrangement outlier detection generalized principal component analysis minimum effective dimension

Mathematics Subject Classification ID

Classification and discrimination; cluster analysis (statistical aspects) (62H30) Image analysis in multivariate analysis (62H35) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Machine vision and scene understanding (68T45)

Related Items (38)

The hierarchy of block models ⋮ Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data ⋮ An inexact splitting method for the subspace segmentation from incomplete and noisy observations ⋮ Unnamed Item ⋮ Hilbert series of subspace arrangements ⋮ A rank-constrained matrix representation for hypergraph-based subspace clustering ⋮ Image clustering based on sparse patch alignment framework ⋮ Subspace segmentation by dense block and sparse representation ⋮ Reprint of: A forward-backward greedy approach for sparse multiscale learning ⋮ Robust algebraic segmentation of mixed rigid-body and planar motions from two views ⋮ Subspace arrangements, configurations of linear spaces and the quadrics containing them ⋮ Minimal basis subspace representation: a unified framework for rigid and non-rigid motion segmentation ⋮ Hybrid linear modeling via local best-fit flats ⋮ A new approach to two-view motion segmentation using global dimension minimization ⋮ Improvement of the fast clustering algorithm improved by \(K\)-means in the big data ⋮ Spectral clustering based on local linear approximations ⋮ Algebraic Identification of MIMO SARX Models ⋮ Realization Theory for Discrete-Time Semi-algebraic Hybrid Systems ⋮ An efficient matrix bi-factorization alternative optimization method for low-rank matrix recovery and completion ⋮ Robust recovery of multiple subspaces by geometric \(l_{p}\) minimization ⋮ Numerical Algorithms on the Affine Grassmannian ⋮ \(\ell\) major component detection and analysis (\(\ell^1\) MCDA): foundations in two dimensions ⋮ Unnamed Item ⋮ Robust subspace clustering ⋮ On the existence of optimal unions of subspaces for data modeling and clustering ⋮ The Grassmannian of affine subspaces ⋮ Learning algebraic varieties from samples ⋮ Foundations of a multi-way spectral clustering framework for hybrid linear modeling ⋮ Optimal non-linear models for sparsity and sampling ⋮ Schubert Varieties and Distances between Subspaces of Different Dimensions ⋮ Linearization of resolutions via products ⋮ Nonlinear least squares in \(\mathbb R^{N}\) ⋮ Self-regularized fixed-rank representation for subspace segmentation ⋮ New robust principal component analysis for joint image alignment and recovery via affine transformations, Frobenius and \(L_{2,1}\) norms ⋮ A forward-backward greedy approach for sparse multiscale learning ⋮ Tensor Methods for Nonlinear Matrix Completion ⋮ Set membership identification of switched linear systems with known number of subsystems ⋮ Filtrated Algebraic Subspace Clustering

This page was built for publication: Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data