Error-correction learning of three layer neural networks based on linear homogeneous expressions

A three-layer neural network (TLNN) in which the nonlinearity of a neuron is of signum is discussed. The author first proposes an expression of the discriminant function of the TLNN, which is called a linear homogeneous expression. This expression allows differentiation in spite of the signum property of the neuron. Subsequently, a learning algorithm is proposed based on the linear homogeneous form. The algorithm is an error-correction procedure, which gives a mathematical foundation to heuristic error-correction learning described in the literature