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
收藏
页数：23
相关论文
共 50 条
  • [31] A class of spectral conjugate gradient methods for Riemannian optimization
    Tang, Chunming
    Tan, Wancheng
    Xing, Shajie
    Zheng, Haiyan
    NUMERICAL ALGORITHMS, 2023, 94 (01) : 131 - 147
  • [32] A Riemannian conjugate gradient method for optimization on the Stiefel manifold
    Xiaojing Zhu
    Computational Optimization and Applications, 2017, 67 : 73 - 110
  • [33] A class of spectral conjugate gradient methods for Riemannian optimization
    Chunming Tang
    Wancheng Tan
    Shajie Xing
    Haiyan Zheng
    Numerical Algorithms, 2023, 94 : 131 - 147
  • [34] Riemannian gradient methods for stochastic composition problems
    Huang, Feihu
    Gao, Shangqian
    NEURAL NETWORKS, 2022, 153 : 224 - 234
  • [35] Combining Conjugate Gradient and Momentum for Unconstrained Stochastic Optimization With Applications to Machine Learning
    Yuan, Yulan
    Tsang, Danny H. K.
    Lau, Vincent K. N.
    IEEE INTERNET OF THINGS JOURNAL, 2024, 11 (13): : 23236 - 23254
  • [36] Conjugate directions for stochastic gradient descent
    Schraudolph, NN
    Graepel, T
    ARTIFICIAL NEURAL NETWORKS - ICANN 2002, 2002, 2415 : 1351 - 1356
  • [37] ON THE CONVERGENCE OF CONJUGATE-GRADIENT ALGORITHMS
    PYTLAK, R
    IMA JOURNAL OF NUMERICAL ANALYSIS, 1994, 14 (03) : 443 - 460
  • [38] Towards stochastic conjugate gradient methods
    Schraudolph, NN
    Graepel, T
    ICONIP'02: PROCEEDINGS OF THE 9TH INTERNATIONAL CONFERENCE ON NEURAL INFORMATION PROCESSING: COMPUTATIONAL INTELLIGENCE FOR THE E-AGE, 2002, : 853 - 856
  • [39] A Riemannian variant of the Fletcher-Reeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendata
    Yao, Teng-Teng
    Bai, Zheng-Jian
    Zhao, Zhi
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2019, 26 (02)
  • [40] SOLVING LARGE AND SPARSE LINEAR LEAST-SQUARES PROBLEMS BY CONJUGATE-GRADIENT ALGORITHMS
    ZLATEV, Z
    NIELSEN, HB
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1988, 15 (03) : 185 - 202
12345