A New Matrix Maximization Model for Computing Ratios of Generalized Singular Values from High-Order GSVD

Wei Wei Xu*, Michael K. Ng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

Abstract

A High-Order Generalized Singular Value Decomposition (HO-GSVD) is employed to compare multiple matrices {Ai}Ni=1 with different row dimensions by using their generalized singular values {σi,k}Ni=1 respectively. The ratio values of σi,k/ σj,k can be used to indicate the significance of the k-th basis vector of the right hand side of matrix from HO-GSVD for multiple matrices {Ai}Ni=1. The main aim of this paper is to propose and study a new matrix maximization model for computing ratios of σi,k/ σj,k from A1, … , AN. The resulting optimization problem can be solved by using Newton method on Lie Groups, and the convergence of the Newton method with well defined initial value can also be established. Numerical examples for synthetic data and mRNA expression data sets are reported to demonstrate the fast performance of the proposed method for solving the optimization model with other existing state-of-the-art algorithms and Riemannian Newton method.

Original languageEnglish
Article number35
Number of pages22
JournalJournal of Scientific Computing
Volume94
Issue number2
Early online date6 Jan 2023
DOIs
Publication statusPublished - Feb 2023

Scopus Subject Areas

  • Theoretical Computer Science
  • Software
  • Numerical Analysis
  • Engineering(all)
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Global and quadratic convergence
  • High-order generalized singular value decomposition
  • Matrix maximization models
  • Newton methods on Lie groups

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