Noise robustness enhancement using fourth-order cumulants cost function

A novel robust fourth-order cumulants cost function is introduced to enhance the fitting to underlying function in small data sets with high noise level of Gaussian noise. The neural network learns based on the gradient descent optimization method by introducing a constraint term in the cost function. The proposed cost function was applied to benchmark sunspot series prediction and nonlinear system identification. Excellent results are obtained. The neural network can provide lower training error and excellent generalization property. Our proposed cost function enables the network to provide, at most, 73% reduction of normalized test error in the benchmark test.