Simultaneous Learning of Several Bayesian Discriminant Functions by a Neural Network with Additional Nodes

We construct a one-hidden-layer neural network which can simultaneously learn several Bayesian discriminant functions. The method can be applied if there exists a common transformation which transforms them to sums of a common main function and simple additional functions respectively. In this paper, we treat concretely the case where the state-conditional probability distributions are normal and the additional simple functions are supposed to be linear. Corresponding to this decomposition, the neural network has a main structure and additional linear nodes.