Fast adaptive principal component extraction based on a generalized energy function

Abstract

By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recursive least squares (RLS) algorithm to extract in parallel multiple principal components of the input covariance matrix without designing an asymmetrical circuit. The local stability of the GEF algorithm at the equilibrium is analytically verified. Simulation results show that the GEF algorithm for parallel multiple principal components extraction exhibits the fast convergence and has the improved robustness resistance to the eigenvalue spread of the input covariance matrix as compared to the well-known lateral inhibition model (APEX) and least mean square error reconstruction (LMSER) algorithms.