On the solutions of one-class-one-outputed feedforward neural network classifiers using backpropagation training

This paper studies the solutions of the outer-supervised batch-style learning based one-class-one-outputed (OCOO) feedforward neural network (FNN) classifiers. It is proven that if the condition of the hidden neuron number is greater than the total training sample number, which is sufficient but not necessary, is satisfied, the network would uniquely converge to the global minima with null costs, and that the condition of the range space of the outer-supervised signal matrix being included in the range space of the hidden output matrix is a sufficient and necessary condition of ensuring local free minima. Furthermore, in the case of the hidden neuron number being smaller than the total training sample number and greater than the output neuron number, it is shown that the global minimum solutions with null costs may also be derived by adequately adjusting the first layer weights. In the case of the hidden neuron number being smaller than the output neuron number, however, it is shown that there would not exist any global minima with null costs in the error surface