Abstract

A methodology has been developed for performing stepwise orthogonal decomposition of a data set using a derivative of the backpropagation neural network algorithm. The network is divided into two parts: a linear orthogonal feature extraction portion, and a nonlinear mapping portion consisting of one or more layers. Error feedback from the nonlinear mapping portion is used to direct the feature extraction process. In addition, the use of multivariate Gaussian kernel function nodes has been generalized to allow inclusion as any backpropagation network node. The derivation of these algorithms is described, and some of their properties are illustrated with controlled artificial data distributions.

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