一个多维次成分并行提取算法及其收敛性分析

A Parallel Multiple Minor Components Extraction Algorithm and Its Convergence Analysis

次成分分析是信号处理领域内一项重要的分析工具.目前,多维次成分并行提取算法数量稀少,而且现有的算法在应用时还存在很多限制条件.针对上述问题,在分析研究OJAm次子空间跟踪算法的基础上,采用加权矩阵法提出了一种多维次成分提取算法,并采用递归最小二乘法对所提算法进行了简化,最后采用李雅普诺夫函数法确定了所提算法的全局收敛域.相比现有算法,所提算法对信号的特征值大小没有要求,也不需要在迭代过程中进行模值归一化操作,同时算法具有较低的计算复杂度.仿真实验表明:所提算法能够并行提取多维次成分,而且收敛速度要优于现有同类型算法.

Minor component analysis is a powerful tool in the field of signal processing. Up to now, there are few algorithms that can extract multiple minor components in parallel.Some existing algorithms have some limitations for real applications. In order to solve these problems, a novel multiple minor components extraction algorithm is proposed by introduing the weighted matrix method into the OJAm minor subspace algorithm. A recursive least square(RLS) algorithm is also derived based on the proposed algorithm. The global convergence region of the proposed algorithm is obtained by using the Lyapunov function method. Compared with some existing algorithms, the proposed algorithm has no restriction on the values of eigenvalue and does not need normalization operation during iterations. Its computation complexity is less than those of some counterparts.Simulation results show that the proposed algorithm can adaptively extract multiple minor components from input signals in parallel and has faster convergence speed than some same-type algorithms.