Adaptive Generalized Eigen-Pairs Extraction Algorithms and Their Convergence Analysis

The generalized Hermitian eigenvalue problem (GHEP) is of great use in modern signal processing. Compared with other methods, neural network model based algorithms provide an efficient way to solve such problems online. Up to now, a class of neural network model based generalized feature extraction algorithms have been reported in the literature. However, most existing noncoupled algorithms suffer from the so-called speed-stability problem. In contrast, coupled learning algorithms estimate the generalized eigenvector and generalized eigenvalue simultaneously in coupled manners. Therefore they can solve the speed-stability problem and perform better than noncoupled algorithms. In this paper, we first propose a coupled generalized system, which is obtained by using the Newton's method and a novel generalized information criterion. Then, based on this coupled generalized system, we successfully obtain two coupled algorithms with normalization steps for minor/principal generalized eigen-pairs extraction. And the technique of multiple generalized eigen-pairs extraction is also introduced in this paper. The convergence of the proposed algorithms is justified by deterministic discrete-time (DDT) approach, with the efficiency and feasibility validated by experimental results as well. Compared with similar work, the proposed algorithms have lower computational complexity, better numerical stability and higher estimation accuracy.