A neural network learning algorithm for adaptive principal component extraction (APEX)

Abstract

The problem of the recursive computation of the principal components of a vector stochastic process is discussed. The applications of this problem arise in modeling of control systems, high-resolution spectrum analysis, image data compression, motion estimation, etc. An algorithm called APEX which can recursively compute the principal components using a linear neural network is proposed. The algorithm is recursive and adaptive: given the first m-1 principal components, it can produce the mth component iteratively. The numerical theoretical basis of the fast convergence of the APEX algorithm is given, and its computational advantages over previously proposed methods are demonstrated. Extension to extracting constrained principal components using APEX is also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>