A robust training of dendritic neuron model neural network for time series prediction

Many prediction methods proposed in the literature can be concerned under two main headings: probabilistic and non-probabilistic methods. In particular, as a kind of non-probabilistic model, artificial neural networks (ANNs), having different properties, have been commonly and effectively used in the literature. Some ANNs operate the additive aggregation function in the structure of their neuron models, while others employ the multiplicative aggregation function. Recently proposed dendritic neural networks also have both additional and multiplicative neuron models. The prediction performance of such an artificial neural network will inevitably be negatively affected by the outliers that the time series of interest may contain due to the neuron model in its structure. This study, for the training of a dendritic neural network, presents a robust learning algorithm. The presented robust algorithm is the first for the training of DNM in the literature as far as is known and uses Huber's loss function as the fitness function. The iterative process of the robust learning algorithm is carried out by particle swarm optimization. The productivity and efficiency of the suggested learning algorithm were evaluated by analysing different real-life time series. All analyses were performed with original and contaminated data sets under different scenarios. The R-DNM has the best performance for the original data sets with a value of 2.95% in the ABC time series, while the FTSE showed the best performance in approximately 27% and the second best in 33% of all analyses. The proposed R-DNM has been the least affected by outliers in almost all scenarios for contaminated ABC data sets. Moreover, it has been the least affected model by outliers in approximately 71% of the 90 analyses performed for the contaminated FTSE time series. The obtained results show that the dendritic artificial neural network trained by the proposed robust learning algorithm produces the satisfactory predictive results in the analysis of time series with and without outliers.