Balancing matrix factorizations via gradient flow techniques and the singular value decomposition

2002 ◽  
Author(s):  
J.E. Perkins ◽  
U. Helmke ◽  
J.B. Moore
Keyword(s):  
Singular Value Decomposition ◽  
Gradient Flow ◽  
Singular Value ◽  
Matrix Factorizations ◽  
Value Decomposition ◽  
Flow Techniques

scholarly journals Continuous analogues of matrix factorizations

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140585 ◽  
Author(s):  
Alex Townsend ◽  
Lloyd N. Trefethen
Keyword(s):  
Singular Value Decomposition ◽  
Infinite Series ◽  
Singular Value ◽  
Matrix Factorizations ◽  
One Dimension ◽  
Continuous Variables ◽  
Triangular Structure ◽  
Column Pivoting ◽  
Value Decomposition ◽  
Cholesky Factorizations

Analogues of singular value decomposition (SVD), QR, LU and Cholesky factorizations are presented for problems in which the usual discrete matrix is replaced by a ‘quasimatrix’, continuous in one dimension, or a ‘cmatrix’, continuous in both dimensions. Two challenges arise: the generalization of the notions of triangular structure and row and column pivoting to continuous variables (required in all cases except the SVD, and far from obvious), and the convergence of the infinite series that define the cmatrix factorizations. Our generalizations of triangularity and pivoting are based on a new notion of a ‘triangular quasimatrix’. Concerning convergence of the series, we prove theorems asserting convergence provided the functions involved are sufficiently smooth.

scholarly journals Some properties of various types of matrix factorization

2021 ◽  
Vol 36 ◽  
pp. 03003
Author(s):  
Wei Shean Ng ◽  
Wei Wen Tan
Keyword(s):  
Pattern Recognition ◽  
Singular Value Decomposition ◽  
Matrix Factorization ◽  
Data Clustering ◽  
Computation Time ◽  
Singular Value ◽  
Cholesky Factorization ◽  
Matrix Factorizations ◽  
Matrix Decompositions ◽  
Value Decomposition

Matrix factorizations or matrix decompositions are methods that represent a matrix as a product of two or more matrices. There are various types of matrix factorizations such as LU factorization, Cholesky factorization, singular value decomposition etc. Matrix factorization is widely used in pattern recognition, image denoising, data clustering etc. Motivated by these applications, some properties and applications of various types of matrix factorizations are studied. One of the purposes of matrix factorization is to ease the computation. Thus, comparisons in term of computation time of various matrix factorizations in different areas are carried out.

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
Sign in / Sign up

Export Citation Format

Share Document