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1. Singular unitary representations and discrete series for indefinite Stiefel manifolds U(p,q;̳F)/U(p-m,q;̳F)
by Kobayashi, Toshiyuki
1992, ISBN 0821825240, Volume no. 462., v, 106
Harmonic analysis | Stiefel manifolds | Semisimple Lie groups | Representations of groups
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2. The topology of Stiefel manifolds
by James, I. M. 1928- (Ioan Mackenzie)
1976, London Mathematical Society lecture note series, ISBN 9780521213349, Volume 24, viii, 168
Stiefel manifolds are an interesting family of spaces much studied by algebraic topologists. These notes, which originated in a course given at Harvard... 
Stiefel manifolds
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3. Full Text Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations
by Balajewicz, Maciej and Tezaur, Irina and Dowell, Earl and Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Journal of Computational Physics, ISSN 0021-9991, 09/2016, Volume 321, Issue C, pp. 224 - 241
For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account.... 
Projection-based reduced order model (ROM) | Stabilization | Stiefel manifold | Trace minimization | Proper Orthogonal Decomposition (POD) | Compressible flow | MATRIX | BOUNDARY-LAYER | POD | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | REDUCTION | DYNAMICS | SYSTEMS | OPTIMIZATION | PROPER ORTHOGONAL DECOMPOSITION | TURBULENT FLOWS | COHERENT STRUCTURES | Turbulence | Models | Mechanical engineering | Analysis | Aerospace engineering | trace minimization | stabilization | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | projection-based reduced order model (ROM) | compressible flow
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4. Topology of manifolds and varieties
by Viro, O. I͡A., 1948
1994, Advances in Soviet mathematics, ISBN 9780821841242, Volume 18, xvii, 284
Manifolds (Mathematics) | Varieties (Universal algebra) | Topology
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5. Full Text Classification of matrix-variate Fisher–Bingham distribution via Maximum Likelihood Estimation using manifold valued data
by Ali, Muhammad and Gao, Junbin
Neurocomputing, ISSN 0925-2312, 06/2018, Volume 295, pp. 72 - 85
In the existing literature, the numerical estimation of multivariate normalizing constant is considered highly non-trivial, intractable or a big barrier to... 
Stiefel manifolds | Grassmann manifolds | SPA | MLE | Classification | Normalization constants | Multivariate Fisher and Bingham distributions | REGRESSION | NEAREST-NEIGHBOR | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VON MISES-FISHER | MODELS | SADDLEPOINT APPROXIMATIONS | NORMALIZING CONSTANT | Usage | Analysis | Algorithms
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6. Full Text Learning Sparse PCA with Stabilized ADMM Method on Stiefel Manifold
by Tan, Mingkui and Hu, Zhibin and Yan, Yuguang and Cao, Jiezhang and Gong, Dong and Wu, Qingyao
IEEE Transactions on Knowledge and Data Engineering, ISSN 1041-4347, 8/2019, pp. 1 - 1
Sparse principal component analysis (SPCA) produces principal components with sparse loadings, which is very important for handling data with many irrelevant... 
Manifolds | Feature selection | Loading | Sparse principal component analysis | Stiefel manifold | Feature extraction | Convex functions | Covariance matrices | ADMM | Optimization | Principal component analysis
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7. Full Text Solving Partial Least Squares Regression via Manifold Optimization Approaches
by Chen, Haoran and Sun, Yanfeng and Gao, Junbin and Hu, Yongli and Yin, Baocai
IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, 02/2019, Volume 30, Issue 2, pp. 588 - 600
Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two data sets. However, all existing approaches... 
Riemannian manifolds | Grassmann manifolds | Linear regression | Partial least squares regression (PLSR) | Riemannian conjugate gradient method | Matrix decomposition | Sun | Optimization | Manifolds | Stiefel manifolds | Classification | Mathematical model | Business | DISTANCE | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | RECOGNITION | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | LOW-RANK REPRESENTATION | PLS | COMPUTER SCIENCE, THEORY & METHODS | GEOMETRY | Riemann manifold | Euclidean geometry | Algorithms | Least squares | Regression | Mathematical models | Euclidean space | Regression analysis
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8. Full Text Localized LRR on Grassmann Manifold: An Extrinsic View
by Wang, Boyue and Hu, Yongli and Gao, Junbin and Sun, Yanfeng and Yin, Baocai
IEEE Transactions on Circuits and Systems for Video Technology, ISSN 1051-8215, 10/2018, Volume 28, Issue 10, pp. 2524 - 2536
Subspace data representation has recently become a common practice in many computer vision tasks. Low-rank representation (LRR) is one of the most successful... 
Manifolds | Computer vision | Symmetric matrices | Grassmann manifold | subspace clustering | Clustering algorithms | Low rank representation | geodesic distance | Data models | Electronic mail | STIEFEL | LOW-RANK REPRESENTATION | NONLINEAR DIMENSIONALITY REDUCTION | ALGORITHM | SEGMENTATION | SUBSPACE | GEOMETRY | ENGINEERING, ELECTRICAL & ELECTRONIC | Clips | State of the art | Handwriting | Algorithms | Mathematical analysis | Digits | Representations | Clustering | Subspaces | Manifolds (mathematics) | Matrix methods
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9. Full Text Advances in matrix manifolds for computer vision
by Lui, Yui Man
Image and Vision Computing, ISSN 0262-8856, 06/2012, Volume 30, Issue 6-7, pp. 380 - 388
The attention paid to matrix manifolds has grown considerably in the computer vision community in recent years. There are a wide range of important... 
Riemannian manifolds | Stiefel manifolds | Grassmann manifolds | Lie groups | RECOGNITION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | VISUAL TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | PEDESTRIAN DETECTION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | 3D MOTION ESTIMATION | OPTIMIZATION | COMPUTER SCIENCE, THEORY & METHODS | OPTICS
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10. Full Text Statistics on the stiefel manifold: Theory and applications
by Chakraborty, Rudrasis and Vemuri, Baba C
Annals of Statistics, ISSN 0090-5364, 02/2019, Volume 47, Issue 1, pp. 415 - 438
A Stiefel manifold of the compact type is often encountered in many fields of engineering including, signal and image processing, machine learning, numerical... 
Gaussian distribution | Homogeneous space | Fréchet mean | Stiefel manifold | DISTRIBUTIONS | SPACE | CENTER-OF-MASS | STATISTICS & PROBABILITY | Frechet mean | RIEMANNIAN-MANIFOLDS | UNIQUENESS | GEOMETRY
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11. Full Text Predictive Quantization on the Stiefel Manifold
by Schwarz, Stefan and Rupp, Markus
IEEE Signal Processing Letters, ISSN 1070-9908, 02/2015, Volume 22, Issue 2, pp. 234 - 238
In this letter, we consider time-varying complex-valued n × m matrices H[k] (m ≤ n) and propose a predictive quantizer for the eigenvectors of the Gramian... 
Manifolds | Quantization (signal) | Transmitters | Grassmann manifold | Adaptive quantization | Stiefel manifold | Signal processing algorithms | Receiving antennas | multi-user MIMO | limited feedback | MIMO | Signal to noise ratio | INTERFERENCE ALIGNMENT | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | BLOCK-DIAGONALIZATION | MATRICES | CONSTRAINTS | DOWNLINK | COMMUNICATION | MIMO BROADCAST CHANNEL | GEOMETRY | Feedback | Quantization | Blocking | Counters | Representations | Channels | Gain
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12. Full Text BAYESIAN NONPARAMETRIC INFERENCE ON THE STIEFEL MANIFOLD
by Lizhen Lin and Vinayak Rao and David Dunson
Statistica Sinica, ISSN 1017-0405, 4/2017, Volume 27, Issue 2, pp. 535 - 553
The Stiefel manifold Vp,d is the space of all d × p orthonormal matrices, with the d−1 hypersphere and the space of all orthogonal matrices constituting... 
Von Mises Fisher | Kernel mixture | Matrix Langevin | Posterior consistency | Stiefel manifold | Orthonormal matrices | Bayesian nonparametric | FISHER DISTRIBUTION | BESSEL-FUNCTIONS | MATRIX | kernel mixture | orthonormal matrices | posterior consistency | DENSITY-ESTIMATION | STATISTICS & PROBABILITY | matrix Langevin | von Mises Fisher
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13. Full Text Manifold properties of planar polygon spaces
by Davis, Donald M
Topology and its Applications, ISSN 0166-8641, 12/2018, Volume 250, pp. 27 - 36
We prove that the tangent bundle of a generic space of planar -gons with specified side lengths, identified under isometry, plus a trivial line bundle is... 
Parallelizability | Tangent bundle | Stiefel–Whitney classes | Polygon spaces | MATHEMATICS | Stiefel-Whitney classes | MATHEMATICS, APPLIED
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14. Full Text Projection-like retractions on matrix manifolds
by Absil, P.-A and Malick, J́er̂ome
SIAM Journal on Optimization, ISSN 1052-6234, 2012, Volume 22, Issue 1, pp. 135 - 158
This paper deals with constructing retractions, a key step when applying optimization algorithms on matrix manifolds. For submanifolds of Euclidean spaces, we... 
Retraction | Spectral manifold | Equality-constrained optimization | Stiefel manifold | Projection | Feasible optimization method | Fixed-rank matrices | Matrix manifold | MATHEMATICS, APPLIED | spectral manifold | MAXIMUM EIGENVALUE FUNCTION | ALGORITHMS | matrix manifold | equality-constrained optimization | retraction | CONSTRAINTS | feasible optimization method | projection | fixed-rank matrices | RIEMANNIAN-MANIFOLDS | Mathematics | Optimization and Control
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15. Full Text Reconstruction of jointly sparse vectors via manifold optimization
by Petrosyan, Armenak and Tran, Hoang and Webster, Clayton
Applied Numerical Mathematics, ISSN 0168-9274, 10/2019, Volume 144, Issue C, pp. 140 - 150
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the... 
Joint sparsity | Non-compact Stiefel manifold | Non-convex optimization | Manifold optimization | Huber regularization | MATHEMATICS, APPLIED | SIGNAL RECONSTRUCTION | Algorithms
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16. Full Text An unconstrained H-2 model order reduction optimisation algorithm based on the Stiefel manifold for bilinear systems
by Xu, KL and Jiang, YL
INTERNATIONAL JOURNAL OF CONTROL, ISSN 0020-7179, 04/2019, Volume 92, Issue 4, pp. 950 - 959
In this paper, the optimal H-2 model order reduction (MOR) problem for bilinear systems is explored. The orthogonality constraint of the cost function... 
INTERPOLATION | the Stiefel manifold | Riemannian metric | model order reduction | cost function | H-2 norm | Bilinear systems | controllability and observability gramians | AUTOMATION & CONTROL SYSTEMS | RIEMANNIAN-MANIFOLDS | GEOMETRY | Euclidean geometry | Algorithms | Cost function | Iterative algorithms | Euclidean space | Model reduction | Iterative methods | Orthogonality | Manifolds (mathematics) | Optimization | System effectiveness
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17. Full Text Reconstruction of jointly sparse vectors via manifold optimization
by Petrosyan, Armenak and Tran, Hoang A and Webster, Clayton G and Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Applied Numerical Mathematics, ISSN 0168-9274, 05/2019, Volume 144, Issue C
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the... 
MATHEMATICS AND COMPUTING | Non-compact Stiefel manifold | Non-convex optimization | Manifold optimization | Huber regularization | Joint sparsity
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18. Full Text Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition
by Turaga, P and Veeraraghavan, A and Srivastava, A and Chellappa, R
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 11/2011, Volume 33, Issue 11, pp. 2273 - 2286
In this paper, we examine image and video-based recognition applications where the underlying models have a special structure-the linear subspace structure. We... 
Manifolds | Geometry | Shape | Face recognition | Computational modeling | feature representation | Humans | statistical models | Grassmann | Data models | Image and video models | Stiefel | manifolds | ILLUMINATION | FACE RECOGNITION | VIEW | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Research | Machine vision | Image processing | Kernel functions | Mathematical optimization | Studies | Images | Inference | Mathematical models | Clustering | Object recognition | Subspaces | Recognition
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19. Full Text Cholesky QR-based retraction on the generalized Stiefel manifold
by Sato, Hiroyuki and Aihara, Kensuke
Computational Optimization and Applications, ISSN 0926-6003, 03/2019, Volume 72, Issue 2, pp. 293 - 308
When optimizing on a Riemannian manifold, it is important to use an efficient retraction, which maps a point on a tangent space to a point on the manifold. In... 
Retraction | Cholesky QR factorization | Generalized Stiefel manifold | Riemannian optimization | MATHEMATICS, APPLIED | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | OPTIMIZATION | ALGORITHMS | RIEMANNIAN-MANIFOLDS | Optimization techniques | Riemann manifold | Maps | Economic impact | Manifolds (mathematics) | Factorization
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20. Full Text Manifold correction method for the nosé-hoover and nosé-poincaré molecular dynamics simulations
by Okumura, Hisashi and Itoh, Satoru G and Ito, Atsushi M and Nakamura, Hiroaki and Fukushima, Toshio
Journal of the Physical Society of Japan, ISSN 0031-9015, 02/2014, Volume 83, Issue 2, p. 24003
We introduce the manifold correction method to molecular dynamics (MD) simulations with the Nose-Hoover and Nose-Poincare thermostats. The manifold correction... 
EFFICIENT ORBIT INTEGRATION | HIGHLY ECCENTRIC ORBITS | KUSTAANHEIMO-STIEFEL REGULARIZATION | PHYSICS, MULTIDISCIPLINARY | MULTIBARIC-MULTITHERMAL ENSEMBLE | KEPLER ENERGY | REPLICA-EXCHANGE METHOD | MULTICANONICAL ENSEMBLE | MONTE-CARLO SIMULATIONS | TEST PARTICLE METHOD | LENNARD-JONES FLUID
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