Wook-Dong Kim

Design of K-means clustering-based polynomial radial basis function neural networks (pRBF NNs) realized with the aid of particle swarm optimization and differential evolution

In this paper, we introduce an advanced architecture of K-means clustering-based polynomial Radial Basis Function Neural Networks (p-RBF NNs) designed with the aid of Particle Swarm Optimization (PSO) and Differential Evolution (DE) and develop a comprehensive design methodology supporting their construction. The architecture of the p-RBF NNs comes as a result of a synergistic usage of the evolutionary optimization-driven hybrid tools. The connections (weights) of the proposed p-RBF NNs being of a certain functional character and are realized by considering four types of polynomials. In order to design the optimized p-RBF NNs, a prototype (center value) of each receptive field is determined by running the K-means clustering algorithm and then a prototype and a spread of the corresponding receptive field are further optimized through running Particle Swarm Optimization (PSO) and Differential Evolution (DE). The Weighted Least Square Estimation (WLSE) is used to estimate the coefficients of the polynomials (which serve as functional connections of the network). The performance of the proposed model and the comparative analysis involving models designed with the aid of PSO and DE are presented in case of a nonlinear function and two Machine Learning (ML) datasets

Fuzzy Radial Basis Function Neural Networks with information granulation and its parallel genetic optimization

Fuzzy modeling of complex systems is a challenging task, which involves important problems of dimensionality reduction and calls for various ways of improving the accuracy of modeling. The IG-FRBFNN, a hybrid architecture of the IG-FIS (Fuzzy Inference System) and FRBFNN (Fuzzy Radial Basis Function Neural Networks), is proposed to address these problems. The paper is concerned with the analysis and design of IG-FRBFNNs and their optimization by means of the Hierarchical Fair Competition-based Parallel Genetic Algorithm (HFC-PGA). In the proposed network, the membership functions of the premise part of the fuzzy rules of the IG-based FRBFNN model directly rely on the computation of the relevant distance between data points and the use of four types of polynomials such as constant, linear, quadratic and modified quadratic are considered for the consequent part of fuzzy rules. Moreover, the weighted Least Square (WLS) learning is exploited to estimate the coefficients of the polynomial forming the conclusion part of the rules. Since the performance of the IG-RBFNN model is affected by some key design parameters, such as a specific subset of input variables, the fuzzification coefficient of the FCM, the number of rules, and the order of polynomial of the consequent part of fuzzy rules, it becomes beneficial to carry out both structural as well as parametric optimization of the network. In this study, the HFC-PGA is used as a comprehensive optimization vehicle. The performance of the proposed model is illustrated by means of several representative numerical examples.

Design of optimized cascade fuzzy controller based on differential evolution: Simulation studies and practical insights

In this study, we discuss a design of an optimized cascade fuzzy controller for the rotary inverted pendulum system and ball & beam system by using an optimization vehicle of differential evolution (DE). The structure of the differential evolution optimization environment is simple and a convergence to optimal values realized here is very good in comparison to the convergence reported for other optimization algorithms. DE is easy to use given its mathematical operators. It also requires a limited computing overhead. The rotary inverted pendulum system and ball & beam system are nonlinear systems, which exhibit unstable motion. The performance of the proposed fuzzy controller is evaluated from the viewpoint of several performance criteria such as overshoot, steady-state error, and settling time. Their values are obtained through simulation studies and practical, real-world experiments. We evaluate and analyze the performance of the proposed optimal fuzzy controller optimized by Genetic Algorithm (GA), and DE. In this setting, we show the superiority of DE versus other methods being used here as well as highlight the characteristics of this optimization tool.

A design of granular-oriented self-organizing hybrid fuzzy polynomial neural networks

In this study, we introduce a new design methodology of granular-oriented self-organizing Hybrid Fuzzy polynomial neural networks (HFPNN) that is based on multi-layer perceptron with context-based polynomial neurons (CPNs) or polynomial neurons (PNs). In contrast to the typical architectures encountered in polynomial neural networks (PNN), our main objective is to develop a design strategy of HFPNN as follows: (a) The first layer of the proposed network consists of context-based polynomial neuron (CPN). Here CPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of context-based fuzzy c-means (C-FCM) clustering method. The context-based clustering supporting the design of information granules is completed in the space of the input data (input variables) while the formation of the clusters here is guided by a collection of some predefined fuzzy sets (so-called contexts) specified in the output space. (b) The proposed design procedure being applied to each layer of HFPNN leads to the selection of the preferred nodes of the network (CPNs or PNs) whose local characteristics (such as the number of contexts, the number of clusters, a collection of the specific subset of input variables, and the order of the polynomial) can be easily adjusted. These options contribute to the flexibility as well as simplicity and compactness of the resulting architecture of the network. For the evaluation of the performance of the proposed HFPNN, we use well-known machine learning data coming from the machine learning repository.

A Design of Dynamically Simultaneous Search GA-based Fuzzy Neural Networks: Comparative Analysis and Interpretation

In this paper, we introduce advanced architectures of genetically-oriented Fuzzy Neural Networks (FNNs) based on fuzzy set and fuzzy relation and discuss a comprehensive design methodology. The proposed FNNs are based on ‘if-then’ rule-based networks with the extended structure of the premise and the consequence parts of the fuzzy rules. We consider two types of the FNNs topologies, called here FSNN and FRNN, depending upon the usage of inputs in the premise of fuzzy rules. Three different type of polynomials function (namely, constant, linear, and quadratic) are used to construct the consequence of the rules. In order to improve the accuracy of FNNs, the structure and the parameters are optimized by making use of genetic algorithms (GAs). We enhance the search capabilities of the GAs by introducing the dynamic variants of genetic optimization. It fully exploits the processing capabilities of the FNNs by supporting their structural and parametric optimization. To evaluate the performance of the proposed FNNs, we exploit a suite of several representative numerical examples and its experimental results are compared with those reported in the previous studies.

Analytic design of information granulation‐based fuzzy radial basis function neural networks with the aid of multiobjective particle swarm optimization

Purpose – The purpose of this paper is to consider the concept of Fuzzy Radial Basis Function Neural Networks with Information Granulation (IG‐FRBFNN) and their optimization realized by means of the Multiobjective Particle Swarm Optimization (MOPSO).Design/methodology/approach – In fuzzy modeling, complexity, interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. Since the performance of the IG‐RBFNN model is directly affected by some parameters, such as the fuzzification coefficient used in the FCM, the number of rules and the orders of the polynomials in the consequent parts of the rules, the authors carry out both structural as well as parametric optimization of the network. A multi‐objective Particle Swarm Optimization using Crowding Distance (MOPSO‐CD) as well as O/WLS learning‐based optimization are exploited to carry out the structural and parametric optimization of the model, respectively, while the optimization is of multiobjective character as i...

Design of radial basis function neural network classifier realized with the aid of data preprocessing techniques: design and analysis

Abstract In this paper, we introduce a new architecture of optimized Radial Basis Function neural network classifier developed with the aid of fuzzy clustering and data preprocessing techniques and discuss its comprehensive design methodology. In the preprocessing part, the Linear Discriminant Analysis (LDA) or Principal Component Analysis (PCA) algorithm forms a front end of the network. The transformed data produced here are used as the inputs of the network. In the premise part, the Fuzzy C-Means (FCM) algorithm determines the receptive field associated with the condition part of the rules. The connection weights of the classifier are of functional nature and come as polynomial functions forming the consequent part. The Particle Swarm Optimization algorithm optimizes a number of essential parameters needed to improve the accuracy of the classifier. Those optimized parameters include the type of data preprocessing, the dimensionality of the feature vectors produced by the LDA (or PCA), the number of clusters (rules), the fuzzification coefficient used in the FCM algorithm and the orders of the polynomials of networks. The performance of the proposed classifier is reported for several benchmarking data-sets and is compared with the performance of other classifiers reported in the previous studies.

Fuzzy set-oriented neural networks based on fuzzy polynomial inference and dynamic genetic optimization

In this paper, we introduce a new topology and offer a comprehensive design methodology of fuzzy set-based neural networks (FsNNs). The proposed architecture of the FsNNs is based on the fuzzy polynomial neurons formed through a collection of ‘if-then’ fuzzy rules, fuzzy inference, and polynomials with the extended structure of the premise and the consequence parts of fuzzy rules being formed within the networks. Three different forms of regression polynomials (namely constant, linear, and quadratic) are used in the consequence part of the rules. In order to build an optimal FsNN, the underlying structural and parametric optimization is supported by a dynamic search-based genetic algorithm (GA), which forms an optimal solution through successive adjustments (refinements) of the search range. The structure optimization involves the determination of the input variables included in the premise part and the order of the polynomial forming the consequence part of the rules. In the study, we explore two types of optimization methodologies, namely a simultaneous tuning and a separate tuning. GAs are global optimizers; however, when being used in their generic version, they often lead to a significant computing overhead caused by the need to explore an excessively large search space. To eliminate this shortcoming and increase the effectiveness of the optimization itself, we introduce a dynamic search-based GA that results in a rapid convergence while narrowing down the search to a limited region of the search space. We exploit this optimization mechanism to be completed both at the structural as well as the parametric level. To evaluate the performance of the proposed FsNN, we offer a suite of several representative numerical examples.

A new approach to radial basis function-based polynomial neural networks: analysis and design

In this study, we introduce a new topology of radial basis function-based polynomial neural networks (RPNNs) that is based on a genetically optimized multi-layer perceptron with radial polynomial neurons (RPNs). This paper offers a comprehensive design methodology involving various mechanisms of optimization, especially fuzzy C-means (FCM) clustering and particle swarm optimization (PSO). In contrast to the typical architectures encountered in polynomial neural networks (PNNs), our main objective is to develop a topology and establish a comprehensive design strategy of RPNNs: (a) The architecture of the proposed network consists of radial polynomial neurons (RPN). These neurons are fully reflective of the structure encountered in numeric data, which are granulated with the aid of FCM clustering. RPN dwells on the concepts of a collection of radial basis function and the function-based nonlinear polynomial processing. (b) The PSO-based design procedure being applied to each layer of the RPNN leads to the selection of preferred nodes of the network whose local parameters (such as the number of input variables, a collection of the specific subset of input variables, the order of the polynomial, the number of clusters of FCM clustering, and a fuzzification coefficient of the FCM method) are properly adjusted. The performance of the RPNN is quantified through a series of experiments where we use several modeling benchmarks, namely a synthetic three-dimensional data and learning machine data (computer hardware data, abalone data, MPG data, and Boston housing data) already used in neuro-fuzzy modeling. A comparative analysis shows that the proposed RPNN exhibits higher accuracy in comparison with some previous models available in the literature.

Design of Optimized Radial Basis Function Neural Networks Classifier with the Aid of Principal Component Analysis and Linear Discriminant Analysis

In this paper, we introduce design methodologies of polynomial radial basis function neural network classifier with the aid of Principal Component Analysis(PCA) and Linear Discriminant Analysis(LDA). By minimizing the information loss of given data, Feature data is obtained through preprocessing of PCA and LDA and then this data is used as input data of RBFNNs. The hidden layer of RBFNNs is built up by Fuzzy C-Mean(FCM) clustering algorithm instead of receptive fields and linear polynomial function is used as connection weights between hidden and output layer. In order to design optimized classifier, the structural and parametric values such as the number of eigenvectors of PCA and LDA, and fuzzification coefficient of FCM algorithm are optimized by Artificial Bee Colony(ABC) optimization algorithm. The proposed classifier is applied to some machine learning datasets and its result is compared with some other classifiers.