一种广义主成分提取算法及其收敛性分析

广义主成分分析在现代信号处理的诸多领域发挥着重要的作用。目前，自适应广义主成分分析算法还并不多见。针对这一现状，该文提出一种快速收敛的广义主成分分析算法，并通过理论分析所提算法的确定性离散时间系统，导出了保证算法收敛的学习因子和初始权向量模值等边界条件。仿真实验和实际应用验证了所提算法的正确性和有用性。仿真结果还表明，所提算法比现有同类算法具有更快的收敛速度和更高的估计精度。

A Generalized Principal Component Extraction Algorithm and Its Convergence Analysis

The generalized principal component analysis plays an important roles in many fields of modern signal processing. However, up to now, there are few algorithms, which can extract the generalized principal component adaptively. In this paper, a generalized principal component extraction algorithm, which has fast convergence speed, is proposed. The corresponding Deterministic Discrete Time (DDT) system of the proposed algorithm is analyzed and some conditions about the learning rate and initial weight vector are also obtained. Finally, computer simulation and practical application results show that compared with some existing algorithms, the proposed algorithm has faster convergence speed and higher estimation accuracy.