主成分计算的改进自然幂迭代方法(英文)  

The Modified Natural Power Method for Principal Component Computation

作　　者：陈天平[1] 马仕钊[1] 

机构地区：[1]复旦大学数学研究所,非线性科学实验室上海200433

出　　处：《复旦学报（自然科学版）》2004年第3期275-284,299,共11页Journal of Fudan University：Natural Science

基　　金：SupportedbyNationalNaturalScienceFoundationofChina(6 9982 0 0 3;6 0 0 74 0 0 5 )

摘　　要：提供快速估计与跟踪一个向量序列的主特征向量的改进自然幂迭代方法 .它是自然幂迭代方法的一个延伸 ,不仅跟踪主子空间 ,而且得到了主特征向量 .与一些基于幂迭代的方法 (例如Oja,PAST与NIC)相比 ,改进自然幂迭代方法具有最快的收敛速度 ,且能容易地以每步迭代O(np)的计算量加以实现 ,这里n为所考虑向量序列的维数 ,p为所要跟踪的主子空间的维数 (或主特征向量的个数 ) .与某些非幂迭代的方法 (例如MAL ASE与OPERA)相比 。A modified version of the natural power method(NP) for fast estimation and tracking of the principal eigenvectors of a vector sequence. It is an extension of the natural power method because it is a solution to obtain the principal eigenvectors as well as to track the principal subspace. Compared with some power-based methods such as Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion(NIC)method, the modified natural power method(MNP) has the fastest convergence rate and can be easily implemented with only O(np) flops of computation at each iteration, where n is the dimension of the vector sequence and p is the dimension of the principal subspace or the number of the principal eigenvectors. Furthermore, it is guaranteed to be globally and exponentially convergent in contrast with some non-power-based methods such as MALASE and OPERA.

关 键 词：主成分计算 微小成分分析 基于幂迭代 指数收敛 快速估计 主特征向量 

分 类 号：O211.6[理学—概率论与数理统计]