TY - JOUR
T1 - A New Matrix Maximization Model for Computing Ratios of Generalized Singular Values from High-Order GSVD
AU - Xu, Wei Wei
AU - Ng, Michael K.
N1 - The research of Wei-Wei Xu is partially supported by the National Natural Science Foundation of China (No. 11971243). The research of Michael K. Ng is partially supported by Hong Kong Research Grant Council GRF 12300218, 12300519, 17201020, 17300021, C1013-21GF, C7004-21GF and Joint NSFC-RGC N-HKU76921.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/2
Y1 - 2023/2
N2 - 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.
AB - 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.
KW - Global and quadratic convergence
KW - High-order generalized singular value decomposition
KW - Matrix maximization models
KW - Newton methods on Lie groups
UR - http://www.scopus.com/inward/record.url?scp=85145684106&partnerID=8YFLogxK
U2 - 10.1007/s10915-022-02071-8
DO - 10.1007/s10915-022-02071-8
M3 - Journal article
AN - SCOPUS:85145684106
SN - 0885-7474
VL - 94
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
M1 - 35
ER -