Concise coupled neural network algorithm for principal component analysis

Abstract

A concise ordinary differential equations (ODE) for eigen-decomposition problem of a symmetric positive matrix is proposed in this paper. Stability properties of the proposed ODE is obtained by the theory of first order approximation. Novel coupled neural network (CNN) algorithm for principal component analysis (PCA) is obtained based on this concise ODE model. Compared with most non-coupled neural PCA algorithms, the proposed online CNN algorithm works in a recursive manner and simultaneously estimates eigenvalue and eigenvector adaptively. Due to the fact the proposed CNN effectively makes use of online eigenvalue estimate during learning process, it reaches a fast convergence speed, which is further verified by the numerical experiment result. Adaptive algorithm for sequential extraction of subsequent principal components is also obtained by means of deflation techniques. © 2008 Springer-Verlag Berlin Heidelberg.