Riemannian Conjugate Gradient Algorithms for Solving λ-Approximation of Stochastic Tensors and Applications

被引：0

作者：

Liu, Dongdong ^{[1
]}

Li, Wen ^{[2
]}

Vong, Seak-Weng ^{[3
]}

Li, Jiaofen ^{[4
]}

Chen, Yannan ^{[2
]}

机构：

[1] Guangdong Univ Technol, Sch Math & Stat, Guangzhou, Peoples R China

[2] South China Normal Univ, Sch Math Sci, Guangzhou, Peoples R China

[3] Univ Macau, Dept Math, Macau, Peoples R China

[4] Guilin Univ Elect Technol, Guangxi Coll & Univ Key Lab Data Anal & Computat, Sch Math & Comp Sci, Guilin, Peoples R China

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2025年 / 32卷 / 02期

基金：

中国国家自然科学基金;

关键词：

higher-order Markov chains; oblique manifold; Riemannian optimization; stochastic tensor;

D O I：

10.1002/nla.70010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose an optimal lambda-approximation model of stochastic tensors arising from higher-order Markov chains. For exploring a fast solver, we first transform the proposed model into a Riemannian optimization problem equivalently. Then we design two Riemannian optimization algorithms for solving the equivalent problem. Finally, some applications to approximate the solution of higher-order Markov chains are given. Several numerical examples including the practical data are given to demonstrate the efficiency of the proposed method.

引用

页数：23

共 50 条

[21] Riemannian Stochastic Recursive Gradient Algorithm
Kasai, Hiroyuki
Sato, Hiroyuki
Mishra, Bamdev
INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 80, 2018, 80
[22] Stochastic Gradient Descent on Riemannian Manifolds
Bonnabel, Silvere
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2013, 58 (09) : 2217 - 2229
[23] A Family of Hybrid Stochastic Conjugate Gradient Algorithms for Local and Global Minimization Problems
Alnowibet, Khalid Abdulaziz
Mahdi, Salem
Alshamrani, Ahmad M.
Sallam, Karam M.
Mohamed, Ali Wagdy
MATHEMATICS, 2022, 10 (19)
[24] The Kernel Conjugate Gradient Algorithms
Zhang, Ming
Wang, Xiaojian
Chen, Xiaoming
Zhang, Anxue
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2018, 66 (16) : 4377 - 4387
[25] Stochastic conjugate gradient inversion
2000, Sci Publ House (35):
[26] Stochastic conjugate gradient inversion
Zhu, Peimin
Wang, Jiaying
Zhan, Zhengbin
Gu, Hanming
Zhu, Guangming
2000, Sci Publ House (35):
[27] STOCHASTIC MODIFIED FLOWS FOR RIEMANNIAN STOCHASTIC GRADIENT DESCENT
Gess, Benjamin
Kassing, Sebastian
Rana, Nimit
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2024, 62 (06) : 3288 - 3314
[28] Stochastic algorithms for solving structured low-rank matrix approximation problems
Gillard, J. W.
Zhigljavsky, A. A.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 21 (1-3) : 70 - 88
[29] A new, globally convergent Riemannian conjugate gradient method
Sato, Hiroyuki
Iwai, Toshihiro
OPTIMIZATION, 2015, 64 (04) : 1011 - 1031
[30] A Riemannian conjugate gradient method for optimization on the Stiefel manifold
Zhu, Xiaojing
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2017, 67 (01) : 73 - 110

← 1 2 3 4 5 →