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Recently, the polynomial-based radial basis function neural networks (P-RBFNNs) have been successfully applied to regression tasks. However, the redundant and non-linear partitioned data easily interfere with accurate partitioning of clusters completed in P-RBFNNs, affecting the regression performance of this existing model. Because the squared error is used as the cost function of the learning method, P-RBFNNs are sensitive to noise interference. In order to cope with these problems, this study introduces a double iterative learning-based polynomial based-RBFNNs (DP-RBFNNs) modeling that focuses on the formation of architectures to improve the accuracy of regression performance as well as enhance the robustness through double iterative learning as follows: a) support vector-based Gaussian kernel fuzzy c-means (SV-GKFCM) as a kind of the support vector-based kernel fuzzy clustering are designed to determine connections (weights) between the input and hidden layers of the proposed model. SV-GKFCM helps effectively reduce the number of redundant data to re-modify the partitioning of clusters in the DP-RBFNNs. In addition, the cluster centers can be accurately updated from the non-linear partitioned data with the aid of Gaussian kernel distance in SV-GKFCM; b) least absolute shrinkage deviations (LASD) as a robust estimation are designed to update connection weights between the hidden and output layers. The SAE (sum of absolute error) function in the LASD method is used as a cost function to reduce the noise interference in the procedure of weight estimation as well as enhance the robustness of the DP-RBFNNs. The superiority of the proposed model is demonstrated through the experimental results. [ABSTRACT FROM AUTHOR]

• We propose fuzzy reinforced polynomial neural networks based on PNN architecture. • We propose fuzzy reinforced polynomial neurons (FRPNs) in the design of FRPNNs. • The proposed FRPNNs is a generalization of hybrid predictors (HPs). In the field of dynamic system identification and prediction, linear models (e.g., autoregressive models), nonlinear models (namely, neural networks models), and hybrid predictors (HPs) that are a hybridization of linear and nonlinear models have been proposed in the past. However, they are not completely free from limitations: they exhibit difficulties to describe high-order nonlinear relations between input and output variables. In this study, we propose fuzzy reinforced polynomial neural networks (FRPNNs), which are polynomial neural network architecture-based on fuzzy reinforced polynomial neurons (FRPNs) to overcome this limitation. The proposed FRPNs that consist of approximation part (AP) and compensation part (CP) arise as novel HPs. Here the CP for modeling nonlinear patterns can be regarded as forming the reinforced part for the AP that aims at capturing linear patterns, while AP is the linear polynomial neuron used in the conventional polynomial neural networks. In some sense, the overall FRPNNs are essentially generalized polynomial neural network architecture with novel HPs. The parameters considered in the design of the proposed fuzzy reinforced polynomial neural networks are optimized with the aid of the particle swarm optimization (PSO). The performance of FRPNNs is discussed involving time series and system identification datasets. Experimental results demonstrate that the proposed FRPNNs achieve at most the accuracy of 43.6% higher in comparison with the accuracy produced by some classical models reported in the literature. [ABSTRACT FROM AUTHOR]

In this study, we propose Hybrid Radial Basis Function Neural Networks (HRBFNNs) realized with the aid of fuzzy clustering method (Fuzzy C-Means, FCM) and polynomial neural networks. Fuzzy clustering used to form information granulation is employed to overcome a possible curse of dimensionality, while the polynomial neural network is utilized to build local models. Furthermore, genetic algorithm (GA) is exploited here to optimize the essential design parameters of the model (including fuzzification coefficient, the number of input polynomial fuzzy neurons (PFNs), and a collection of the specific subset of input PFNs) of the network. To reduce dimensionality of the input space, principal component analysis (PCA) is considered as a sound preprocessing vehicle. The performance of the HRBFNNs is quantified through a series of experiments, in which we use several modeling benchmarks of different levels of complexity (different number of input variables and the number of available data). A comparative analysis reveals that the proposed HRBFNNs exhibit higher accuracy in comparison to the accuracy produced by some models reported previously in the literature. [ABSTRACT FROM AUTHOR]