The radial basis function RBF network has its foundation in the conventional approximation theory. It has the capability of universal approximation. The RBF network is a popular alternative to the well-known multilayer perceptron MLP , since it has a simpler structure and a much faster training process. In this paper, we give a comprehensive survey on the RBF network and its learning. Many aspects associated with the RBF network, such as network structure, universal approximation capability, radial basis functions, RBF network learning, structure optimization, normalized RBF networks, application to dynamic system modeling, and nonlinear complex-valued signal processing, are described. We also compare the features and capability of the two models.

Many information processing problems can be transformed into some form of eigenvalue or singular value problems. Eigenvalue decomposition (EVD) and singular value decomposition (SVD) are usually used for solving these problems. In this paper, we give an introduction to various neural network implementations and algorithms for principal component analysis (PCA) and its various extensions. PCA is a statistical method that is directly related to EVD and SVD. Minor component analysis (MCA) is a variant of PCA, which is useful for solving total least squares (TLSs) problems. The algorithms are typical unsupervised learning methods. Some other neural network models for feature extraction, such as localized methods, complex-domain methods, generalized EVD, and SVD, are also described. Topics associated with PCA, such as independent component analysis (ICA) and linear discriminant analysis (LDA), are mentioned in passing in the conclusion. These methods are useful in adaptive signal processing, blind signal separation (BSS), pattern recognition, and information compression.

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