主成分计算的改进自然幂迭代方法

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MALASE与OPERA)相比，改进自然幂迭代方法保证了全局指数收敛．

The Modified Natural Power Method forPrincipal Component Computation

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.