Objective Function and Learning Algorithm for the General Node Fault Situation

Fault tolerance is one interesting property of artificial neural networks. However, the existing fault models are able to describe limited node fault situations only, such as stuck-at-zero and stuck-at-one. There is no general model that is able to describe a large class of node fault situations. This paper studies the performance of faulty radial basis function (RBF) networks for the general node fault situation. We first propose a general node fault model that is able to describe a large class of node fault situations, such as stuck-at-zero, stuck-at-one, and the stuck-at level being with arbitrary distribution. Afterward, we derive an expression to describe the performance of faulty RBF networks. An objective function is then identified from the formula. With the objective function, a training algorithm for the general node situation is developed. Finally, a mean prediction error (MPE) formula that is able to estimate the test set error of faulty networks is derived. The application of the MPE formula in the selection of basis width is elucidated. Simulation experiments are then performed to demonstrate the effectiveness of the proposed method.