Generalized eigenvalue decomposition has many advantages when it is applied in modern signal processing. Compared with other methods, neural network model-based algorithms provide an efficient way to solve such problems online. Generalized feature extraction algorithms based on neural network models have been described in the literature. However, the majority of the existing algorithms can only extract the principal generalized eigenvector(s) or eigensubspace. To extract principal and minor generalized eigenvectors from two vector sequences, in this paper, two different information criteria are proposed, and a unified algorithm for the extraction of multiple components in a parallel way by simply altering the sign is derived based on these information criteria, which is feasible for generalized principal and minor component analysis. Moreover, all the corresponding principal and minor generalized eigenvalues can be extracted simultaneously because the desired equilibrium point depends on these values. Thus, the proposed algorithm can perform multiple generalized eigenpair extraction. The proposed algorithm possesses four properties: unification, self-stability, parallel extraction and generalized eigenpair extraction, that few of the existing algorithms can encompass. The global convergence and self-stability property of the proposed algorithm are proved through the Lyapunov method and ordinary differential equation method, respectively. The proposed algorithm has a fast convergence speed, high precision and strong tracking ability. Finally, numerical examples and applications are explored to further demonstrate the efficiency of the proposed algorithm.

中文翻译：

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多重广义特征对提取的统一自稳定并行算法

广义特征值分解在现代信号处理中具有许多优点。与其他方法相比，基于神经网络模型的算法提供了一种在线解决此类问题的有效方法。文献中已经描述了基于神经网络模型的广义特征提取算法。然而，大多数现有算法只能提取主要的广义特征向量或特征子空间。为了从两个向量序列中提取主次广义特征向量，本文提出了两种不同的信息标准，并基于这些信息标准推导出一种通过简单改变符号并行提取多个分量的统一算法，这对于广义主成分和次成分分析是可行的。而且，所有相应的主要和次要广义特征值都可以同时提取，因为所需的平衡点取决于这些值。因此，所提出的算法可以执行多个广义特征对提取。所提出的算法具有四个特性：统一性、自稳定性、并行提取和广义特征对提取，这是现有算法中很少有的。分别通过Lyapunov方法和常微分方程方法证明了该算法的全局收敛性和自稳定性。该算法收敛速度快、精度高、跟踪能力强。最后，探讨了数值例子和应用，以进一步证明所提出算法的效率。