A multistage representation of the Wiener filter based on orthogonal projections
IEEE Transactions on Information Theory
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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) [7] 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 [2] 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.