Convergence Analysis of a Kind of Deterministic Discrete-Time PCA Algorithm

We proposed a generalized adaptive learning rate (GALR) PCA algorithm, which could be guaranteed that the algorithm’s convergence process would not be affected by the selection of the initial value. Using the deterministic discrete time (DDT) method, we gave the upper and lower bounds of the algorithm and proved the global convergence. Numerical experiments had also verified our theory, and the algorithm is effective for both online and offline data. We found that choosing different initial vectors will affect the convergence speed, and the initial vector could converge to the second or third eigenvectors by satisfying some exceptional conditions.