Abstract: At present, most principal component analysis (PCA) algorithms based on neural networks are considered non-coupled algorithms, which suffer from the so-called speed-stability problem. In recent years, a few coupled algorithms have been proposed, and these algorithms can mitigate the speed-stability problem of most non-coupled algorithms. However, these coupled algorithms still suffer from problems such as a complex derivation process and highly complex expression. In this paper, we propose two coupled PCA algorithms based on a novel information criterion and by modifying Newton's method, and we analyze the convergence of algorithms by using Jacobian matrix. Compared with existing coupled algorithms, the proposed algorithms can be obtained easily without the need to calculate the inverse Hessian matrix. Simulation experiments validate the favorable capability of the proposed algorithms.