Optimized feature extraction and the Bayes decision in feed-forward classifier networks

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Abstract
The problem of multiclass pattern classification using adaptive layered networks is addressed. A special class of networks, i.e., feed-forward networks with a linear final layer, that perform generalized linear discriminant analysis is discussed, This class is sufficiently generic to encompass the behavior of arbitrary feed-forward nonlinear networks. Training the network consists of a least-square approach which combines a generalized inverse computation to solve for the final layer weights, together with a nonlinear optimization scheme to solve for parameters of the nonlinearities. A general analytic form for the feature extraction criterion is derived, and it is interpreted for specific forms of target coding and error weighting. An important aspect of the approach is to exhibit how a priori information regarding nonuniform class membership, uneven distribution between train and test sets, and misclassification costs may be exploited in a regularized manner in the training phase of networks.