正交性
数学
收敛速度
算法
跟踪(心理语言学)
趋同(经济学)
正定矩阵
应用数学
二次方程
多元统计
数学优化
计算机科学
统计
特征向量
物理
几何学
经济
哲学
频道(广播)
量子力学
计算机网络
经济增长
语言学
作者
Jiao‐fen Li,Ya-qiong Wen,Xue‐lin Zhou,Kai Wang
摘要
This paper develops two novel and fast Riemannian second-order approaches for solving a class of matrix trace minimization problems with orthogonality constraints, which is widely applied in multivariate statistical analysis. The existing majorization method is guaranteed to converge but its convergence rate is at best linear. A hybrid Riemannian Newton-type algorithm with both global and quadratic convergence is proposed firstly. A Riemannian trust-region method based on the proposed Newton method is further provided. Some numerical tests and application to the least squares fitting of the DEDICOM model and the orthonormal INDSCAL model are given to demonstrate the efficiency of the proposed methods. Comparisons with some latest Riemannian gradient-type methods and some existing Riemannian second-order algorithms in the MATLAB toolbox Manopt are also presented.
科研通智能强力驱动
Strongly Powered by AbleSci AI