Singular Value Decomposition Learning on Double Stiefel Manifold
نویسنده
چکیده
The aim of this paper is to present a unifying view of four SVD-neural-computation techniques found in the scientific literature and to present some theoretical results on their behavior. The considered SVD neural algorithms are shown to arise as Riemannian-gradient flows on double Stiefel manifold and their geometric and dynamical properties are investigated with the help of differential geometry.
منابع مشابه
Optical Flow Estimation via Neural Singular Value Decomposition Learning
In the recent contribution [9], it was given a unified view of four neuralnetwork-learning-based singular-value-decomposition algorithms, along with some analytical results that characterize their behavior. In the mentioned paper, no attention was paid to the specific integration of the learning equations which appear under the form of first-order matrix-type ordinary differential equations on ...
متن کاملMultiple point of self-transverse immesions of certain manifolds
In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...
متن کاملAnalyzing Magnification Factors and Principal Spread Directions in Manifold Learning
Great amount of data under varying intrinsic features is thought of as high dimensional nonlinear manifold in the observation space. How to analyze the mapping relationship between the high dimensional manifold and the corresponding intrinsic low dimensional one quantitatively is important to machine learning and cognitive science. In this paper, we propose SVD (singular value decomposition) ba...
متن کاملMotion Estimation in Computer Vision: Optimization on Stiefel Manifolds
Motion recovery from image correspondences is typically a problem of optimizing an objective function associated with the epipolar (or LonguetHiggins) constraint. This objective function is defined on the so called essential manifold. In this paper, the intrinsic Riemannian structure of the essential manifold is thoroughly studied. Based on existing optimization techniques on Riemannian manifol...
متن کاملRobust Orthogonal Complement Principal Component Analysis
Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel rob...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- International journal of neural systems
دوره 13 3 شماره
صفحات -
تاریخ انتشار 2003