Winsorized dendritic neuron model artificial neural network and a robust training algorithm with Tukey’s biweight loss function based on particle swarm optimization

Multilayer perceptron artificial neural networks, which are one of the most popular artificial neural network models, are affected by outliers in the data set because they have both additive and multiplicative aggregation functions. From this point of view, neural networks such as Pi-Sigma and multiplicative neuron model artificial neural networks, which have either or both of these functions and have fewer parameters than the multilayer perceptron, are also affected by outliers. It is inevitable that dendritic neuron model artificial neural networks will also be affected by outliers because they also have additive and multiplicative aggregation functions. In this study, a new winsorized dendritic neuron model artificial neural network is proposed. In this new neural network, the winsorized mean in the dendrite layer of the dendritic neuron model artificial neural network is used to reduce the outlier effect in the output. Moreover, a robust learning algorithm based on Tukey’s biweight loss function is proposed for the first time in the literature for a winsorized dendritic neuron model artificial neural network. For the model to work even better in the presence of outliers, a robust standardization method is used to reduce the outlier effect in the input. Besides, the particle swarm optimization method is used in the training of the proposed artificial neural network. The performance of proposed method is performed by analyzing the opening values of the S&P 500 time series in different years for both the original state and the outlier state. As a result of the analyses made, it is concluded that the proposed method is not affected by the outliers in the data set, but the other methods compared with the proposed method are affected by the outliers in the data set.