A novel noise robust fourth-order cumulants cost function

A novel robust fourth-order cumulants cost function was introduced to enhance the fitting to an underlying function in small data sets with high noise level of Gaussian distribution because higher-order statistics provide a unique feature of suppressing Gaussian noise processes of unknown spectral characteristics. The proposed cost function was validated on the prediction of benchmark sunspot data and an excellent result was obtained. The proposed cost function enables the network to provide a very low training error and an excellent generalization property, Our result indicates that the network trained by the proposed cost function can, at most, provide 74% reduction of the normalized test error in the benchmark test.