Link between adaptive feed-forward layered networks and discriminant analysis

摘要

Abstract: The paper expands the available theoretical framework that establishes a link between an adaptive feedforward layered linear-output network used as a mean-square classifier and discriminant analysis. We prove that, under reasonable assumptions, minimizing the mean- square error at the network output is equivalent to minimizing the following: (1) the difference between the optimum value of a familiar discriminant criterion and the value of this criterion evaluated in the space spanned by the outputs of the final hidden layer, and (2) the difference between the values of the same discriminant criterion evaluated in desired-output and actual- output subspaces. We also illustrate, under specific constraints, how to solve the following problem: given a feature extraction criterion, how the target coding scheme can be selected such that this criterion is maximized at the output of the network final hidden layer.!7