On pattern classification using linear-output neural network classifiers

This paper provides theoretical results regarding the use of linear-output neural networks as mean-square classifiers. The paper first proves that, under reasonable assumptions, once training is complete, the minimized sample mean-square error equals the difference between the value of a familiar discriminant criterion evaluated in a network target subspace and its value evaluated either in the network hidden space or in a network output subspace. This result directly indicates that for linear-output BP networks minimizing the error is equivalent to minimizing the difference between the values of this discriminant criterion evaluated in the relevant spaces. Two experimental illustrations are given. The paper then derives the complete set of constraints satisfied by the weights, the outputs, and the biases of the linear output layer