منابع مشابه
Bayesian inference on the Stiefel manifold
The Stiefel manifold Vp,d is the space of all d×p orthonormal matrices, and includes the d−1 hypersphere and the space of all orthogonal matrices as special cases. It is often desirable to parametrically or nonparametrically estimate the distribution of variables taking values on this manifold. Unfortunately, the intractable normalizing constant in the likelihood makes Bayesian inference challe...
متن کاملQuadratic programs over the Stiefel manifold
We characterize the optimal solution of a quadratic program over the Stiefel manifold with an objective function in trace formulation. The result is applied to relaxations of HQAP and MTLS. Finally, we show that strong duality holds for the Lagrangian dual, provided some redundant constraints are added to the primal program. © 2005 Elsevier B.V. All rights reserved.
متن کاملMultivariate Regression via Stiefel Manifold Constraints
We introduce a learning technique for regression between highdimensional spaces. Standard methods typically reduce this task to many onedimensional problems, with each output dimension considered independently. By contrast, in our approach the feature construction and the regression estimation are performed jointly, directly minimizing a loss function that we specify, subject to a rank constrai...
متن کاملOn minimizing a quadratic function on Stiefel manifold
Article history: Received 3 October 2014 Accepted 17 February 2015 Available online 9 March 2015 Submitted by J.F. Queiro MSC: 90C22 15A39 90C20
متن کاملA low complexity Lie group method on the Stiefel manifold
A low complexity Lie group method for numerical integration of ordinary differential equations on the orthogonal Stiefel manifold is presented. Based on the quotient space representation of the Stiefel manifold we provide a representation of the tangent space suitable for Lie group methods. According to this representation a special type of generalized polar coordinates (GPC) is defined and use...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 1996
ISSN: 0926-2245
DOI: 10.1016/0926-2245(96)89145-5