A Constructive Algorithm for Feedforward Neural Networks With Incremental Training

Abstract—We develop, in this brief, a new constructive learning algorithm for feedforward neural networks. We employ an incremental training procedure where training patterns are learned one by one. Our algorithm starts with a single training pattern and a single hidden-layer neuron. During the course of neural network training, when the algorithm gets stuck in a local minimum, we will attempt to escape from the local minimum by using the weight scaling technique. It is only after several consecutive failed attempts in escaping from a local minimum that will we allow the network to grow by adding a hidden-layer neuron. At this stage, we employ an optimization procedure based on quadratic/linear programming to select initial weights for the newly added neuron. Our optimization procedure tends to make the network reach the error tolerance with no or little training after adding a hidden-layer neuron. Our simulation results indicate that the present constructive algorithm can obtain neural networks very close to minimal structures (with the least possible number of hidden-layer neurons) and that convergence (to a solution) in neural network training can be guaranteed. We tested our algorithm extensively using a widely used benchmark problem, i.e., the parity problem. Index Terms—Constructive algorithm, feedforward neural networks, incremental training, linear programming, quadratic programming. I