基于不等概自适应抽样和随机SVD分解的CUR矩阵重构  

CUR Matrix Decomposition Based on Unequal Probability Adaptive Sampling and Stochastic SVD Decomposition

作　　者：任潇潇 牛成英 REN Xiao-xiao;NIU Cheng-ying(Lanzhou University of Finance and Economics,Lanzhou 730020,China)

机构地区：[1]兰州财经大学,甘肃兰州730020

出　　处：《数理统计与管理》2024年第2期280-294,共15页Journal of Applied Statistics and Management

基　　金：国家社会科学基金项目(21BTJ042);兰州财经大学科研创新团队支持计划资助。

摘　　要：高维大数据矩阵分析中,使用少量主要成分逼近原始数据矩阵是常用方法,这些主要成分是矩阵行和列的线性组合,不易对数据的原始特征进行解释。本文提出将不等概抽样与自适应抽样结合的适用于CUR矩阵分解的抽样方法,并将该抽样方法与矩阵随机奇异值分解(SVD)方法相结合,对抽样得到的列矩阵C和行矩阵R进行随机SVD分解,在控制计算复杂度的同时提高低秩逼近重构矩阵的精度。研究结果表明,在矩阵低秩逼近中,基于不等概自适应抽样和随机SVD分解相结合的CUR矩阵分解方法具有较高的精确度和稳定性。In high-dimensional big data matrix analysis,it is a common method to approximate the original data matrix with a few major components.These major components are linear combinations of matrix rows and columns,and it is difficult to explain the original characteristics of the data.Proposed in this paper to be ranging sampling combined with adaptive sampling method is suitable for the CUR matrix decomposition,and the random sampling method and matrix singular value decomposition(SVD)method,combining the matrix C and R obtained by sampling randomly SVD decomposition,in the control of computational complexity and improve the accuracy of low rank approximation reconstruction.The results show that the CUR matrix decomposition method based on the combination of unequal probability adaptive sampling and stochastic SVD decomposition has high accuracy and stability in lowrank approximation of matrices.

关 键 词：CUR矩阵分解方法 不等概自适应抽样 随机SVD分解 相对误差 计算复杂度 

分 类 号：O212[理学—概率论与数理统计]