A flag representation for finite collections of subspaces of mixed dimensions

DOI10.1016/j.laa.2014.03.022zbMath1326.14118OpenAlexW1993570538WikidataQ125933139 ScholiaQ125933139MaRDI QIDQ2451200

Yanyan Li

Publication date: 3 June 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2014.03.022

zbMATH Keywords

flag manifoldSVDGrassmann manifoldmultiset canonical correlation analysisextrinsic manifold meanflag meansubspace average

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Eigenvalues, singular values, and eigenvectors (15A18) Statistical aspects of information-theoretic topics (62B10) Cyclic codes (94B15) Local Riemannian geometry (53B20)

Related Items (8)

The max‐length‐vector line of best fit to a set of vector subspaces and an optimization problem over a set of hyperellipsoids ⋮ Geometric Metrics for Topological Representations ⋮ Angle-based joint and individual variation explained ⋮ Schubert Varieties and Distances between Subspaces of Different Dimensions ⋮ Expected distances on manifolds of partially oriented flags ⋮ Joint and individual analysis of breast cancer histologic images and genomic covariates ⋮ Random Triangles and Polygons in the Plane ⋮ Flag Manifolds for the Characterization of Geometric Structure in Large Data Sets

Uses Software

• CMU PIE

Cites Work

• A learning algorithm for adaptive canonical correlation analysis of several data sets
• The Geometry of Flag Manifolds
• Riemannian center of mass and mollifier smoothing
• The Geometry of Algorithms with Orthogonality Constraints
• Bayesian and geometric subspace tracking
• Quantization on the Grassmann Manifold
• Numerical Methods for Computing Angles Between Linear Subspaces
• Means and Averaging in the Group of Rotations
• Consensus Optimization on Manifolds
• Canonical analysis of several sets of variables

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