A L-BFGS Based Learning Algorithm for Complex-Valued Feedforward Neural Networks

Abstract

In this paper, a new learning algorithm is proposed for complex-valued feedforward neural networks (CVFNNs). The basic idea of this algorithm is that the descent directions of the cost function with respect to complex-valued parameters are calculated by limited-memory BFGS algorithm and the learning step is determined by Armijo line search method. Since the approximation of Hessian matrix is calculated by utilizing the information of the latest several iterations, the memory efficiency is improved. To keep away from the saturated ranges of activation functions, some gain parameters are adjusted together with weights and biases. Compared with some existing learning algorithms for CVFNNs, the convergence speed is faster and a deeper minima of the cost function can be reached by the developed algorithm. In addition, the effects of initial values of weights and biases on the efficiency and convergence speed of the learning algorithm are analyzed. The performance of the proposed algorithm is evaluated in comparison with some existing classifiers on a variety of benchmark classification problems. Experimental results show that better performance is achieved by our algorithm with relatively compact network structure.