• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.4
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• pp.862-870
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• 2011

In this paper, we introduce a new topology of Radial Basis Function-based Polynomial Neural Networks (RPNN) that is based on a genetically optimized multi-layer perceptron with Radial Polynomial Neurons (RPNs). This study offers a comprehensive design methodology involving mechanisms of optimization algorithms, especially Fuzzy C-Means (FCM) clustering method and Particle Swarm Optimization (PSO) algorithms. In contrast to the typical architectures encountered in Polynomial Neural Networks (PNNs), our main objective is to develop a design strategy of RPNNs as follows : (a) The architecture of the proposed network consists of Radial Polynomial Neurons (RPNs). In here, the RPN is fully reflective of the structure encountered in numeric data which are granulated with the aid of Fuzzy C-Means (FCM) clustering method. The 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 at each layer of RPNN leads to the selection of preferred nodes of the network (RPNs) whose local characteristics (such as the number of input variables, a collection of the specific subset of input variables, the order of the polynomial, and the number of clusters as well as a fuzzification coefficient in the FCM clustering) can be easily adjusted. The performance of the RPNN is quantified through the experimentation where we use a number of modeling benchmarks - NOx emission process data of gas turbine power plant and learning machine data(Automobile Miles Per Gallon Data) already experimented with in fuzzy or neurofuzzy modeling. A comparative analysis reveals that the proposed RPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

• Proceedings of the IEEK Conference
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• 2009.05a
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• pp.261-263
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• 2009

본 연구에서는 복잡한 비선형 모델링 방법인 RBF 뉴럴 네트워크(Radial Basis Function Neural Network)와 PNN(Polynomial Neural Network)을 접목한 새로운 형태의 Radial Basis Function Polynomial Neural Network(RPNN)를 제안한다. RBF 뉴럴 네트워크는 빠른 학습 시간, 일반화 그리고 단순화의 특징으로 비선형 시스템 모델링 등에 적용되고 있으며, PNN은 생성된 노드들 중에서 우수한 결과값을 가진 노드들을 선택함으로써 모델의 근사화 및 일반화에 탁월한 효과를 가진 비선형 모델링 방법이다. 제안된 RPNN모델의 기본적인 구조는 PNN의 형태를 이루고 있으며, 각각의 노드는 RBF 뉴럴 네트워크로 구성하였다. 사용된 RBF 뉴럴 네트워크에서의 커널 함수로는 FCM 클러스터링을 사용하였으며, 각 노드의 후반부는 다항식 구조로 표현하였다. 또한 각 노드의 후반부 파라미터들은 최소자승법을 이용하여 최적화 하였다. 제안한 모델의 적용 및 유용성을 비교 평가하기 위하여 비선형 데이터를 이용하여 그 우수성을 보인다.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.11
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• pp.2108-2116
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• 2008

The paper concerns Fuzzy C-Means clustering based Radial Basis Function neural networks (FCM-RBFNN) and the optimization of the network is carried out by means of Particle Swarm Optimization(PSO). FCM-RBFNN is the extended architecture of Radial Basis Function Neural Network(RBFNN). In the proposed network, the membership functions of the premise part of fuzzy rules do not assume any explicit functional forms such as Gaussian, ellipsoidal, triangular, etc., so its resulting fitness values directly rely on the computation of the relevant distance between data points by means of FCM. Also, as the consequent part of fuzzy rules extracted by the FCM - RBFNN model, the order of four types of polynomials can be considered such as constant, linear, quadratic and modified quadratic. Weighted Least Square Estimator(WLSE) are used to estimates the coefficients of polynomial. Since the performance of FCM-RBFNN is affected by some parameters of FCM-RBFNN such as a specific subset of input variables, fuzzification coefficient of FCM, the number of rules and the order of polynomials of consequent part of fuzzy rule, we need the structural as well as parametric optimization of the network. In this study, the PSO is exploited to carry out the structural as well as parametric optimization of FCM-RBFNN. Moreover The proposed model is demonstrated with the use of numerical example and gas furnace data set.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.1 no.3
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• pp.69-76
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• 2008

This paper concerns Fuzzy Radial Basis Function Neural Network (FRBFNN) and automatic rule generation of extraction of the FRBFNN by means of mountain clustering. In the proposed network, the membership functions of the premise part of fuzzy rules do not assume any explicit functional forms such as Gaussian, ellipsoidal, triangular, etc., so its resulting fitness values (degree of membership) directly rely on the computation of the relevant distance between data points. Also, we consider high-order polynomial as the consequent part of fuzzy rules which represent input-output characteristic of sup-space. The number of clusters and the centers of clusters are automatically generated by using mountain clustering method based on the density of data. The centers of cluster which are obtained by using mountain clustering are used to determine a degree of membership and weighted least square estimator (WLSE) is adopted to estimate the coefficients of the consequent polynomial of fuzzy rules. The effectiveness of the proposed model have been investigated and analyzed in detail for the representative nonlinear function.

• Journal of Electrical Engineering and Technology
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• v.9 no.6
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• pp.2098-2106
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• 2014

In the area of clustering, there are numerous approaches to construct clusters in the input space. For regression problem, when forming clusters being a part of the overall model, the relationships between the input space and the output space are essential and have to be taken into consideration. Conditional Fuzzy C-Means (c-FCM) clustering offers an opportunity to analyze the structure in the input space with the mechanism of supervision implied by the distribution of data present in the output space. However, like other clustering methods, c-FCM focuses on the distribution of the data. In this paper, we introduce a new method, which by making use of the ambiguity index focuses on the boundaries of the clusters whose determination is essential to the quality of the ensuing classification procedures. The introduced design is illustrated with the aid of numeric examples that provide a detailed insight into the performance of the fuzzy classifiers and quantify several essentials design aspects.

• Proceedings of the KIEE Conference
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• 2007.10a
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• pp.451-452
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• 2007

본 논문에서는 다항식 기반 Radial Basis Function(RBF)신경회로망(Polynomial based Radial Basis Function Neural Networks)을 설계하고 이를 2-클래스 패턴 분류 문제에 응용하여 그 성능을 분석한다. 제안된 다항식기반 RBF 신경회로망은 입력층, 은닉층, 출력 층으로 이루어진다. 입력층은 입력 벡터의 값들을 은닉 층으로 전달하는 기능을 수행하고 은닉층은 Fuzzy c-means 클러스터링을 통하여 뉴런의 출력 값으로 내보낸다. 은닉층과 출력층사이의 연결가중치는 상수, 선형식 또는 이차식으로 이루어지며 경사 하강법에 의해 학습된다. Networks의 최종 출력은 연결가중치와 은닉층 출력의 곱에 의해 퍼지추론의 결과로서 얻어진다. 제안된 다항식기반 RBF 신경회로망은 각기 다른 4종류의 2-클래스 분류 문제에 적용 및 평가되어 분류기로써의 성능을 분석한다.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.10
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• pp.1469-1478
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• 2015

In this paper, The methodology of Type-2 fuzzy set-based Radial Basis Function Neural Network(T2RBFNN) is proposed for Sewage Treatment Process and the simulator is developed for application to the real-world sewage treatment plant by using the proposed model. The proposed model has robust characteristic than conventional RBFNN. architecture of network consist of three layers such as input layer, hidden layer and output layer of RBFNN, and Type-2 fuzzy set is applied to receptive field in contrast with conventional radial basis function. In addition, the connection weights of the proposed model are defined as linear polynomial function, and then are learned through Back-Propagation(BP). Type reduction is carried out by using Karnik and Mendel(KM) algorithm between hidden layer and output layer. Sewage treatment data obtained from real-world sewage treatment plant is employed to evaluate performance of the proposed model, and their results are analyzed as well as compared with those of conventional RBFNN.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.2
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• pp.399-406
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• 2009

In this study, Polynomial Radial Basis Function Neural Network(pRBFNN) based on Fuzzy Inference System is designed and its parameters such as learning rate, momentum coefficient, and distributed weight (width of RBF) are optimized by means of Particle Swarm Optimization. The proposed model can be expressed as three functional module that consists of condition part, conclusion part, and inference part in the viewpoint of fuzzy rule formed in 'If-then'. In the condition part of pRBFNN as a fuzzy rule, input space is partitioned by defining kernel functions (RBFs). Here, the structure of kernel functions, namely, RBF is generated from HCM clustering algorithm. We use Gaussian type and Inverse multiquadratic type as a RBF. Besides these types of RBF, Conic RBF is also proposed and used as a kernel function. Also, in order to reflect the characteristic of dataset when partitioning input space, we consider the width of RBF defined by standard deviation of dataset. In the conclusion part, the connection weights of pRBFNN are represented as a polynomial which is the extended structure of the general RBF neural network with constant as a connection weights. Finally, the output of model is decided by the fuzzy inference of the inference part of pRBFNN. In order to evaluate the proposed model, nonlinear function with 2 inputs, waster water dataset and gas furnace time series dataset are used and the results of pRBFNN are compared with some previous models. Approximation as well as generalization abilities are discussed with these results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.12
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• pp.2352-2360
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• 2011

In this paper, we introduce a comprehensive design methodology of Radial Basis Function Neural Networks (RBFNN) that is based on mechanism of clustering and optimization algorithm. We can divide some clusters based on similarity of input dataset by using clustering algorithm. As a result, the number of clusters is equal to the number of nodes in the hidden layer. Moreover, the centers of each cluster are used into the centers of each receptive field in the hidden layer. In this study, we have applied Fuzzy-C Means(FCM) and K-Means(KM) clustering algorithm, respectively and compared between them. The weight connections of model are expanded into the type of polynomial functions such as linear and quadratic. In this reason, the output of model consists of relation between input and output. In order to get the optimal structure and better performance, Particle Swarm Optimization(PSO) is used. We can obtain optimized parameters such as both the number of clusters and the polynomial order of weights connection through structural optimization as well as the widths of receptive fields through parametric optimization. To evaluate the performance of proposed model, NXT equipment offered by National Instrument(NI) is exploited. The situation awareness system-related intelligent model was built up by the experimental dataset of distance information measured between object and diverse sensor such as sound sensor, light sensor, and ultrasonic sensor of NXT equipment.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.6
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• pp.735-740
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• 2012

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.