Gradient Algorithm on Stiefel Manifold and Application in Feature Extraction
نویسندگان
چکیده
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 کاملA Riemannian conjugate gradient method for optimization on the Stiefel manifold
In this paper we propose a new Riemannian conjugate gradient method for optimization on the Stiefel manifold. We introduce two novel vector transports associated with the retraction constructed by the Cayley transform. Both of them satisfy the Ring-Wirth nonexpansive condition, which is fundamental for convergence analysis of Riemannian conjugate gradient methods, and one of them is also isomet...
متن کاملStatistics on the (compact) Stiefel manifold: Theory and Applications
A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space but not a symmetric space. In previous work, researchers have defined probability distributions on symmetric spaces and performed statistical analysis of data ...
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 کاملNeural Learning and Weight Flow on Stiefel Manifold
The aim of this paper is to present a new class of learning models for linear as well as non-linear neural layers called Orthonormal StronglyConstrained (SOC or Stiefel). They allow to solve orthonormal problems where orthonormal matrices are involved. After general properties of the learning rules belonging to this new class are shown, examples derived independently or by reviewing learning th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: JOURNAL OF RADARS
سال: 2014
ISSN: 2095-283X
DOI: 10.3724/sp.j.1300.2013.13048