A new discrete-continuous algorithm for radial basis function networks construction

Data-Knowledge-Driven Self-Organizing Fuzzy Neural Network

Fuzzy neural networks (FNNs) hold the advantages of knowledge leveraging and adaptive learning, which have been widely used in nonlinear system modeling. However, it is difficult for FNNs to obtain the appropriate structure in the situation of insufficient data, which limits its generalization performance. To solve this problem, a data-knowledge-driven self-organizing FNN (DK-SOFNN) with a structure compensation strategy and a parameter reinforcement mechanism is proposed in this article. First, a structure compensation strategy is proposed to mine structural information from empirical knowledge to learn the structure of DK-SOFNN. Then, a complete model structure can be acquired by sufficient structural information. Second, a parameter reinforcement mechanism is developed to determine the parameter evolution direction of DK-SOFNN that is most suitable for the current model structure. Then, a robust model can be obtained by the interaction between parameters and dynamic structure. Finally, the proposed DK-SOFNN is theoretically analyzed on the fixed structure case and dynamic structure case. Then, the convergence conditions can be obtained to guide practical applications. The merits of DK-SOFNN are demonstrated by some benchmark problems and industrial applications.

Fast Multi-Objective Antenna Optimization Based on RBF Neural Network Surrogate Model Optimized by Improved PSO Algorithm

In this paper, a radial basis function neural network (RBFNN) surrogate model optimized by an improved particle swarm optimization (PSO) algorithm is developed to reduce the computation cost of traditional antenna design methods which rely on high-fidelity electromagnetic (EM) simulations. Considering parameters adjustment and update mechanism simultaneously, two modifications are proposed in this improved PSO. First, time-varying learning factors are designed to balance exploration and exploitation ability of particles in the search space. Second, the local best information is added to the updating process of particles except for personal and global best information for better population diversity. The improved PSO is applied to train RBFNN for determining optimal network parameters. As a result, the constructed improved PSO-RBFNN model can be used as a surrogate model for antenna performance prediction with better network generalization capability. By integrating the improved PSO-RBFNN surrogate model with multi-objective evolutionary algorithms (MOEAs), a fast multi-objective antenna optimization framework for multi-parameter antenna structures is then established. Finally, a Pareto-optimal planar miniaturized multiband antenna design is presented, demonstrating that the proposed model provides better prediction performance and considerable computational savings compared to those previously published approaches.

Self-Organizing RBF Neural Network Using an Adaptive Gradient Multiobjective Particle Swarm Optimization

One of the major obstacles in using radial basis function (RBF) neural networks is the convergence toward local minima instead of the global minima. For this reason, an adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm is designed to optimize both the structure and parameters of RBF neural networks in this paper. First, the AGMOPSO algorithm, based on a multiobjective gradient method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance. Second, the AGMOPSO-based self-organizing RBF neural network (AGMOPSO-SORBF) can optimize the parameters (centers, widths, and weights), as well as determine the network size. The goal of AGMOPSO-SORBF is to find a tradeoff between the accuracy and the complexity of RBF neural networks. Third, the convergence analysis of AGMOPSO-SORBF is detailed to ensure the prerequisite of any successful applications. Finally, the merits of our proposed approach are verified on multiple numerical examples. The results indicate that the proposed AGMOPSO-SORBF achieves much better generalization capability and compact network structure than some other existing methods.

An Efficient Second-Order Algorithm for Self-Organizing Fuzzy Neural Networks

Intelligent computing technologies are useful and important for online data modeling, where system dynamics may be nonstationary with some uncertainties. In this paper, an efficient learning mechanism is developed for building self-organizing fuzzy neural networks (SOFNNs), where a second-order algorithm (SOA) with adaptive learning rate is employed, the network size and the parameters can be determined simultaneously in the learning process. First, all parameters of SOFNN are adjusted by using the SOA strategy to achieve fast convergence through a powerful search scheme. Second, the structure of SOFNN can be self-organized using the relative importance index of each rule. The fuzzy rules used in SOFNN with SOA (SOA-SOFNN) are generated or pruned automatically to reduce the computational complexity and potentially improve the generalization power. Finally, a theoretical analysis on the learning convergence of the proposed SOA-SOFNN is given to show the computational efficiency. To demonstrate the merits of our proposed approach for data modeling, several benchmark datasets, and a real world application associated with nonlinear systems modeling problems are examined with comparisons against other existing methods. The results indicate that our proposed SOA-SOFNN performs favorably in terms of both learning speed and prediction accuracy for online data modeling.

New Discrete-Time ZNN Models for Least-Squares Solution of Dynamic Linear Equation System With Time-Varying Rank-Deficient Coefficient

In this brief, a new one-step-ahead numerical differentiation rule called six-instant -cube finite difference (6I CFD) formula is proposed for the first-order derivative approximation with higher precision than existing finite difference formulas (i.e., Euler and Taylor types). Subsequently, by exploiting the proposed 6I CFD formula to discretize the continuous-time Zhang neural network model, two new-type discrete-time ZNN (DTZNN) models, namely, new-type DTZNNK and DTZNNU models, are designed and generalized to compute the least-squares solution of dynamic linear equation system with time-varying rank-deficient coefficient in real time, which is quite different from the existing ZNN-related studies on solving continuous-time and discrete-time (dynamic or static) linear equation systems in the context of full-rank coefficients. Specifically, the corresponding dynamic normal equation system, of which the solution exactly corresponds to the least-squares solution of dynamic linear equation system, is elegantly introduced to solve such a rank-deficient least-squares problem efficiently and accurately. Theoretical analyses show that the maximal steady-state residual errors of the two new-type DTZNN models have an pattern, where denotes the sampling gap. Comparative numerical experimental results further substantiate the superior computational performance of the new-type DTZNN models to solve the rank-deficient least-squares problem of dynamic linear equation systems.

A Novel Recurrent Neural Network for Manipulator Control With Improved Noise Tolerance

In this paper, we propose a novel recurrent neural network to resolve the redundancy of manipulators for efficient kinematic control in the presence of noises in a polynomial type. Leveraging the high-order derivative properties of polynomial noises, a deliberately devised neural network is proposed to eliminate the impact of noises and recover the accurate tracking of desired trajectories in workspace. Rigorous analysis shows that the proposed neural law stabilizes the system dynamics and the position tracking error converges to zero in the presence of noises. Extensive simulations verify the theoretical results. Numerical comparisons show that existing dual neural solutions lose stability when exposed to large constant noises or time-varying noises. In contrast, the proposed approach works well and has a low tracking error comparable to noise-free situations.

An Adaptive-PSO-Based Self-Organizing RBF Neural Network

In this paper, a self-organizing radial basis function (SORBF) neural network is designed to improve both accuracy and parsimony with the aid of adaptive particle swarm optimization (APSO). In the proposed APSO algorithm, to avoid being trapped into local optimal values, a nonlinear regressive function is developed to adjust the inertia weight. Furthermore, the APSO algorithm can optimize both the network size and the parameters of an RBF neural network simultaneously. As a result, the proposed APSO-SORBF neural network can effectively generate a network model with a compact structure and high accuracy. Moreover, the analysis of convergence is given to guarantee the successful application of the APSO-SORBF neural network. Finally, multiple numerical examples are presented to illustrate the effectiveness of the proposed APSO-SORBF neural network. The results demonstrate that the proposed method is more competitive in solving nonlinear problems than some other existing SORBF neural networks.

Improving Neural-Network Classifiers Using Nearest Neighbor Partitioning

This paper presents a nearest neighbor partitioning method designed to improve the performance of a neural-network classifier. For neural-network classifiers, usually the number, positions, and labels of centroids are fixed in partition space before training. However, that approach limits the search for potential neural networks during optimization; the quality of a neural network classifier is based on how clear the decision boundaries are between classes. Although attempts have been made to generate floating centroids automatically, these methods still tend to generate sphere-like partitions and cannot produce flexible decision boundaries. We propose the use of nearest neighbor classification in conjunction with a neural-network classifier. Instead of being bound by sphere-like boundaries (such as the case with centroid-based methods), the flexibility of nearest neighbors increases the chance of finding potential neural networks that have arbitrarily shaped boundaries in partition space. Experimental results demonstrate that the proposed method exhibits superior performance on accuracy and average f-measure.

Data Generators for Learning Systems Based on RBF Networks

There are plenty of problems where the data available is scarce and expensive. We propose a generator of semiartificial data with similar properties to the original data, which enables the development and testing of different data mining algorithms and the optimization of their parameters. The generated data allow large-scale experimentation and simulations without danger of overfitting. The proposed generator is based on radial basis function networks, which learn sets of Gaussian kernels. These Gaussian kernels can be used in a generative mode to generate new data from the same distributions. To assess the quality of the generated data, we evaluated the statistical properties of the generated data, structural similarity, and predictive similarity using supervised and unsupervised learning techniques. To determine usability of the proposed generator we conducted a large scale evaluation using 51 data sets. The results show a considerable similarity between the original and generated data and indicate that the method can be useful in several development and simulation scenarios. We analyze possible improvements in the classification performance by adding different amounts of the generated data to the training set, performance on high-dimensional data sets, and conditions when the proposed approach is successful.