A Multistage Decomposition Approach for Adaptive Principal Component Analysis

摘要

This paper devises a novel neural network model applied to finding the principal components of a N -dimensional data stream. This neural network consists of r (≤ N ) neurons, where the i -th neuron has only N — i +1 weights and a N — i +1 dimensional input vector that is obtained by the multistage dimension-reduced processing (multistage decomposition) for the input vector sequence and orthogonal to the space spanned by the first i — 1 principal components. All the neurons are trained by the conventional Oja's learning algorithms so as to get a series of dimension-reduced principal components in which the dimension number of the i-th principal component is N — i +1. By systematic reconstruction technique, we can recover all the principal components from a series of dimension-reduced ones. We study its global convergence and show its performance via some simulations. Its remarkable advantage is that its computational complexity is reduced and its weight storage is saved.