A least third-order cumulants objective function

A novel Least Cumulants Method is proposed to tackle the problem of fitting to underlying function in small data sets with high noise level because higher-order statistics provide an unique feature of suppressing Gaussian noise processes of unknown spectral characteristics. The current backpropagation algorithm is actually the Least Square Method based algorithm which does not perform very well in noisy data set. Instead, the proposed method is more robust to the noise because a complete new objective function based on higher-order statistics is introduced. The proposed objective function was validated by applying to predict benchmark sunspot data and excellent results are obtained. The proposed objective function enables the network to provide a very low training error and excellent generalization property. Our results indicate that the network trained by the proposed objective function can, at most, provide 73% reduction of normalized test error in the benchmark test. © 1996 Kluwer Academic Publishers.