Singular Value Decomposition Learning on Double Stiefel Manifold

2003 ◽  
Vol 13 (03) ◽  
pp. 155-170 ◽  
Author(s):  
Simone Fiori
Keyword(s):  
Differential Geometry ◽  
Singular Value Decomposition ◽  
Scientific Literature ◽  
Singular Value ◽  
Neural Computation ◽  
Stiefel Manifold ◽  
Gradient Flows ◽  
Dynamical Properties ◽  
Value Decomposition ◽  
Theoretical Results

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.

scholarly journals A Unified Scalable Equivalent Formulation for Schatten Quasi-Norms

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1325
Author(s):  
Fanhua Shang ◽  
Yuanyuan Liu ◽  
Fanjie Shang ◽  
Hongying Liu ◽  
Lin Kong ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Computational Cost ◽  
Singular Value ◽  
Weighted Sum ◽  
Equivalent Formulation ◽  
Norm Minimization ◽  
The Mean ◽  
Value Decomposition ◽  
High Computational Cost ◽  
Theoretical Results

The Schatten quasi-norm is an approximation of the rank, which is tighter than the nuclear norm. However, most Schatten quasi-norm minimization (SQNM) algorithms suffer from high computational cost to compute the singular value decomposition (SVD) of large matrices at each iteration. In this paper, we prove that for any p, p1, p2>0 satisfying 1/p=1/p1+1/p2, the Schatten p-(quasi-)norm of any matrix is equivalent to minimizing the product of the Schatten p1-(quasi-)norm and Schatten p2-(quasi-)norm of its two much smaller factor matrices. Then, we present and prove the equivalence between the product and its weighted sum formulations for two cases: p1=p2 and p1≠p2. In particular, when p>1/2, there is an equivalence between the Schatten p-quasi-norm of any matrix and the Schatten 2p-norms of its two factor matrices. We further extend the theoretical results of two factor matrices to the cases of three and more factor matrices, from which we can see that for any 0<p<1, the Schatten p-quasi-norm of any matrix is the minimization of the mean of the Schatten (⌊1/p⌋+1)p-norms of ⌊1/p⌋+1 factor matrices, where ⌊1/p⌋ denotes the largest integer not exceeding 1/p.

Improving TF-IDF with Singular Value Decomposition (SVD) for Feature Extraction on Twitter

2017 ◽  
Author(s):  
Ammar Ismael Kadhim ◽  
Yu-N Cheah ◽  
Inaam Abbas Hieder ◽  
Rawaa Ahmed Ali
Keyword(s):  
Feature Extraction ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Value Decomposition

Multi-scale singular value decomposition polarization image fusion defogging algorithm and experiment

2020 ◽  
Vol 13 (6) ◽  
pp. 1-10
Author(s):  
ZHOU Wen-zhou ◽  
◽  
FAN Chen ◽  
HU Xiao-ping ◽  
HE Xiao-feng ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Image Fusion ◽  
Singular Value ◽  
Multi Scale ◽  
Polarization Image ◽  
Value Decomposition
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