A Principal Component Estimation Algorithm with Adaptive Learning Rate and Its Convergence Analysis

The deterministic discrete-time method is a dominant approach for analyzing neural network algorithms. To address the issue where conventional convergence conditions impose stringent restrictions on the range of learning factors, this paper proposes a principal component estimation algorithm with an adaptive learning factor, which guarantees global convergence. The convergence of the algorithm is analyzed using the deterministic discrete-time method, and conditions ensuring convergence are established. Unlike convergence conditions for other algorithms, the proposed algorithm’s convergence conditions eliminate restrictions on the learning factor, thereby extending its feasible range. Simulation results demonstrate that the proposed algorithm effectively resolves ill-conditioned matrix problems. When compared with existing algorithms, the proposed algorithm exhibits significantly faster convergence speed than several current methods.