广义低秩回归的数值方法  

A Numerical Method for General Reduced Rank Regression

作　　者：郑航 刘新国[1] Zheng Hang;Liu Xinguo(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2022年第S01期102-106,共5页Periodical of Ocean University of China

基　　金：国家自然科学基金项目(11871444)资助。

摘　　要：低秩回归模型作为一种降维技术,在多个领域得到了广泛的应用,如信号处理(也称为降秩维纳滤波)、神经网络(也称为非对称PCA)、时间序列分析和计算机视觉。本文研究了广义低秩回归问题,给出了其通解表达式,还给出了解唯一的条件,研究了极小酉不变范数解,进而运用MM思想给出一种数值解法,并用数值实验验证了其有效性。As a dimension reduction technology, low-rank regression model has been widely used in many fields, such as signal processing(also known as reduced-rank Wiener filtering), neural network(also known as asymmetric PCA), time series analysis and computer vision. In this paper, we study the generalized low-rank regression problem, its general solution expression and the unique condition of solution are given. are given the minimal unitary invariant norm solution is studied, and then a numerical solution is given by using MM idea, and its effectiveness is verified by numerical experiments.

关 键 词：低秩回归 极小酉不变范数解 MM方法 

分 类 号：O175[理学—数学]