• International Journal of Control, Automation, and Systems
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• v.2 no.2
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• pp.189-200
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• 2004

In this paper, we introduce a new soft computing technique that dwells on the ideas of combining fuzzy rules in a fuzzy system with polynomial neural networks (PNN). The PNN is a flexible neural architecture whose structure is developed through the modeling process. Unfortunately, the PNN has a fatal drawback in that it cannot be constructed for nonlinear systems with only a small amount of input variables. To overcome this limitation in the conventional PNN, we employed one of three principal soft computing components such as a fuzzy system. As such, a space of input variables is partitioned into several subspaces by the fuzzy system and these subspaces are utilized as new input variables to the PNN architecture. The proposed soft computing technique is achieved by merging the fuzzy system and the PNN into one unified framework. As a result, we can find a workable synergistic environment and the main characteristics of the two modeling techniques are harmonized. Thus, the proposed method alleviates the problems of PNN while providing superb performance. Identification results of the three-input nonlinear static function and nonlinear system with two inputs will be demonstrated to demonstrate the performance of the proposed approach.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.1
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• pp.43-50
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• 2001

In this paper, we propose the design procedure of advance Polynomial Neural Networks(PNN) architecture for optimal model identification of complex and nonlinear system. The proposed PNN architecture is presented as the generic and advanced type. The essence of the design procedure dwells on the Group Method of Data Handling(GMDH). PNN is a flexible neural architecture whose structure is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. In this sense, PNN is a self-organizing network. With the aid of three representative numerical examples, compari-sons show that the proposed advanced PNN algorithm can produce the model with higher accuracy than previous other works. And performance index related to approximation and generalization capabilities of model is evaluated and also discussed.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2891-2893
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• 2005

In this paper, we introduce a new category of Self-Organizing Fuzzy Polynomial Neural Networks (SOFPNN) that is based on a genetically optimized multi-layer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization. The conventional SOFPNN algorithm leads to a tendency to produce overly complex networks as well as a repetitive computation load by the trial and error method and/or the a repetitive parameter adjustment by designer. In order to generate a structurally and parametrically optimized network, such parameters need to be optimal. In this study, in solving the problems with the conventional SOFPNN, we introduce a new design approach of evolutionary optimized SOFPNN. Optimal parameters design available within FPN (viz. the no. of input variables, the order of the polynomial, input variables, and the no. of membership function) lead to structurally and parametrically optimized network which is more flexible as well as simpler architecture than the conventional SOFPNN. In addition, we determine the initial apexes of membership functions by genetic algorithm.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.2
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• pp.398-406
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• 2011

In this paper, we introduce a new architecture of PSO-based Polynomial Neural Networks (PNN) and discuss its comprehensive design methodology. The conventional PNN is based on a extended Group Method of Data Handling (GMDH) method, and utilized the polynomial order (viz. linear, quadratic, and modified quadratic) as well as the number of node inputs fixed (selected in advance by designer) at Polynomial Neurons located in each layer through a growth process of the network. Moreover it does not guarantee that the conventional PNN generated through learning results in the optimal network architecture. The PSO-based PNN results in a structurally optimized structure and comes with a higher level of flexibility that the one encountered in the conventional PNN. The PSO-based design procedure being applied at each layer of PNN leads to the selection of preferred PNs with specific local characteristics (such as the number of input variables, input variables, and the order of the polynomial) available within the PNN. In the sequel, two general optimization mechanisms of the PSO-based PNN are explored: the structural optimization is realized via PSO whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the PSO-based PNN, the model is experimented with using Gas furnace process data, and pH neutralization process data. For the characteristic analysis of the given entire data with non-linearity and the construction of efficient model, the given entire system data is partitioned into two type such as Division I(Training dataset and Testing dataset) and Division II(Training dataset, Validation dataset, and Testing dataset). A comparative analysis shows that the proposed PSO-based PNN is model with higher accuracy as well as more superb predictive capability than other intelligent models presented previously.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.7
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• pp.70-78
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• 1992

In this paper, an approach for 3-D object segmentation and classification, which is based on eigen-values of polynomial function as their surface features, using neural network is proposed. The range images of 3-D objects are classified into surface primitives which are homogeneous in their intrinsic eigenvalue properties. The misclassified regions due to noise effect are merged into correct regions satisfying homogeneous constraints of Hopfield neural network. The proposed method has advantage of processing both segmentation and classification simultaneously.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.970-976
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• 2007

In this study, Polynomial Network Pattern Classifier(PNC) based on Fuzzy Inference Mechanism is designed and its parameters such as learning rate, momentum coefficient and fuzzification coefficient are optimized by means of Particle Swarm Optimization. The proposed PNC employes a partition function created by Fuzzy C-means(FCM) clustering as an activation function in hidden layer and polynomials weights between hidden layer and output layer. Using polynomials weights can help to improve the characteristic of the linear classification of basic neural networks classifier. In the viewpoint of linguistic analysis, the proposed classifier is expressed as a collection of "If-then" fuzzy rules. Namely, architecture of networks is constructed by three functional modules that are condition part, conclusion part and inference part. The condition part relates to the partition function of input space using FCM clustering. In the conclusion part, a polynomial function caries out the presentation of a partitioned local space. Lastly, the output of networks is gotten by fuzzy inference in the inference part. The proposed PNC generates a nonlinear discernment function in the output space and has the better performance of pattern classification as a classifier, because of the characteristic of polynomial based fuzzy inference of PNC.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.7
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• pp.378-388
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• 2000

In this paper, we propose Fuzzy Polynomial Neural Networks(FPNN) based on Polynomial Neural Networks(PNN) and Fuzzy Neural Networks(FNN) for model identification of complex and nonlinear systems. The proposed FPNN is generated from the mutually combined structure of both FNN and PNN. The one and the other are considered as the premise part and consequence part of FPNN structure respectively. As the consequence part of FPNN, PNN is based on Group Method of Data Handling(GMDH) method and its structure is similar to Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and self-organizing networks that can be generated. FPNN is available effectively for multi-input variables and high-order polynomial according to the combination of FNN with PNN. Accordingly it is possible to consider the nonlinearity characteristics of process and to get better output performance with superb predictive ability. As the premise part of FPNN, FNN uses both the simplified fuzzy inference as fuzzy inference method and error back-propagation algorithm as learning rule. The parameters such as parameters of membership functions, learning rates and momentum coefficients are adjusted using genetic algorithms. And we use two kinds of FNN structure according to the division method of fuzzy space of input variables. One is basic FNN structure and uses fuzzy input space divided by each separated input variable, the other is modified FNN structure and uses fuzzy input space divided by mutually combined input variables. In order to evaluate the performance of proposed models, we use the nonlinear function and traffic route choice process. The results show that the proposed FPNN can produce the model with higher accuracy and more robustness than any other method presented previously. And also performance index related to the approximation and prediction capabilities of model is evaluated and discussed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.3 no.3
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• pp.309-330
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• 2009

In this paper, we introduce the architecture of Genetic Algorithm(GA) based Feed-forward Polynomial Neural Networks(PNNs) and discuss a comprehensive design methodology. A conventional PNN consists of Polynomial Neurons, or nodes, located in several layers through a network growth process. In order to generate structurally optimized PNNs, a GA-based design procedure for each layer of the PNN leads to the selection of preferred nodes(PNs) with optimal parameters available within the PNN. To evaluate the performance of the GA-based PNN, experiments are done on a model by applying Medical Imaging System(MIS) data to a multi-variable software process. A comparative analysis shows that the proposed GA-based PNN is modeled with higher accuracy and more superb predictive capability than previously presented intelligent models.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.3
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• pp.639-647
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• 2011

In this paper, we introduce a design methodology of data-centroid Radial Basis Function neural networks with extended polynomial function. The two underlying design mechanisms of such networks involve K-means clustering method and Particle Swarm Optimization(PSO). The proposed algorithm is based on K-means clustering method for efficient processing of data and the optimization of model was carried out using PSO. In this paper, as the connection weight of RBF neural networks, we are able to use four types of polynomials such as simplified, linear, quadratic, and modified quadratic. Using K-means clustering, the center values of Gaussian function as activation function are selected. And the PSO-based RBF neural networks results in a structurally optimized structure and comes with a higher level of flexibility than the one encountered in the conventional RBF neural networks. The PSO-based design procedure being applied at each node of RBF neural networks leads to the selection of preferred parameters with specific local characteristics (such as the number of input variables, a specific set of input variables, and the distribution constant value in activation function) available within the RBF neural networks. To evaluate the performance of the proposed data-centroid RBF neural network with extended polynomial function, the model is experimented with using the nonlinear process data(2-Dimensional synthetic data and Mackey-Glass time series process data) and the Machine Learning dataset(NOx emission process data in gas turbine plant, Automobile Miles per Gallon(MPG) data, and Boston housing data). For the characteristic analysis of the given entire dataset with non-linearity as well as the efficient construction and evaluation of the dynamic network model, the partition of the given entire dataset distinguishes between two cases of Division I(training dataset and testing dataset) and Division II(training dataset, validation dataset, and testing dataset). A comparative analysis shows that the proposed RBF neural networks produces model with higher accuracy as well as more superb predictive capability than other intelligent models presented previously.

• Proceedings of the KIEE Conference
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• 2006.10c
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• pp.217-219
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• 2006

본 연구는 정보입자와 유전알고리즘의 기호코딩을 통해 퍼지집합 기반 다항식 뉴럴네트워크(IG based gFSPNN)의 최적 설계 제안한다. 기존의 Furry Srt-based Polynomial Neural Networks의 최적설계를 위해 유전자 알고리즘의 이진코딩을 사용하였다. 이지코딩은 스티링 길이 때문에 연산시간이 급격히 증가되는 현상과 해밍절벽(Hamming Cliff)에 따른 급격한 비트변환이 힘들다는 단점이 내제 하였다. 이에 본 논문에서는 스티링 길이와 해밍절벽에 따른 문제를 해결 하기위해 기호코딩을 사용하였다._데이터들의 특성을 모델에 반영하기 위해 Hard C-Means(HCM)을 결합한 Information Granulation(IG)을 사용하여 최적모델 구축 속도를 빠르게 하였다. 실험적 예제를 통하여 제안된 모델의 성능을 평가한다.