• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2762-2764
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• 2001

In this study, we introduce and investigate a class of dynamic perceptron architectures, discuss a comprehensive design methodology and carry out a series of numeric experiments. The proposed dynamic perceptron architectures are called as Polynomial Neural Networks(PNN). PNN is a flexible neural architecture whose topology is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated on the fly. In this sense, PNN is a self-organizing network. PNN has two kinds of networks, Polynomial Neuron(FPN)-based and Fuzzy Polynomial Neuron(FPN)-based networks, according to a polynomial structure. The essence of the design procedure of PN-based Self-organizing Polynomial Neural Networks(SOPNN) dwells on the Group Method of Data Handling (GMDH) [1]. Each node of the SOPNN exhibits a high level of flexibility and realizes a polynomial type of mapping (linear, quadratic, and cubic) between input and output variables. FPN-based SOPNN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulations involve a series of synthetic as well as experimental data used across various neurofuzzy systems. A detailed comparative analysis is included as well.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.4
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• pp.327-332
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• 2005

We investigatea new fuzzy-neural networks-Hybrid Fuzzy set based polynomial Neural Networks (HFSPNN). These networks consist of genetically optimized multi-layer with two kinds of heterogeneous neurons thatare fuzzy set based polynomial neurons (FSPNs) and polynomial neurons (PNs). We have developed a comprehensive design methodology to determine the optimal structure of networks dynamically. The augmented genetically optimized HFSPNN (namely gHFSPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of gHFSPNN leads to the selection leads to the selection of preferred nodes (FSPNs or PNs) available within the HFSPNN. In the sequel, the structural optimization is realized via GAs, whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFSPNN is quantified through experimentation where we use a number of modeling benchmarks synthetic and experimental data already experimented with in fuzzy or neurofuzzy modeling.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.9
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• pp.430-438
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• 2001

In this study, we introduce the adaptive Polynomial Neuro-Fuzzy Networks(PNFN) architecture generated from the fusion of fuzzy inference system and PNN algorithm. The PNFN dwells on the ideas of fuzzy rule-based computing and neural networks. Fuzzy inference system is applied in the 1st layer of PNFN and PNN algorithm is employed in the 2nd layer or higher. From these the multilayer structure of the PNFN is constructed. In order words, in the Fuzzy Inference System(FIS) used in the nodes of the 1st layer of PNFN, either the simplified or regression polynomial inference method is utilized. And as the premise part of the rules, both triangular and Gaussian like membership function are studied. In the 2nd layer or higher, PNN based on GMDH and regression polynomial is generated in a dynamic way, unlike in the case of the popular multilayer perceptron structure. That is, the PNN is an analytic technique for identifying nonlinear relationships between system's inputs and outputs and is a flexible network structure constructed through the successive generation of layers from nodes represented in partial descriptions of I/O relatio of data. The experiment part of the study involves representative time series such as Box-Jenkins gas furnace data used across various neurofuzzy systems and a comparative analysis is included as well.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.1
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• pp.40-49
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• 2004

In this paper, we propose a new architecture of Genetic Algorithms(GAs)-based Self-Organizing Polynomial Neural Networks(SOPNN), discuss a comprehensive design methodology and carry out a series of numeric experiments. The conventional SOPNN is based on the 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 (or nodes) located in each layer through a growth process of the network. Moreover it does not guarantee that the SOPNN generated through learning has the optimal network architecture. But the proposed GA-based SOPNN enable the architecture to be a structurally more optimized network, and to be much more flexible and preferable neural network than the conventional SOPNN. In order to generate the structurally optimized SOPNN, GA-based design procedure at each stage (layer) of SOPNN leads to the selection of preferred nodes (or PNs) with optimal parameters- such as the number of input variables, input variables, and the order of the polynomial-available within SOPNN. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the model. A detailed design procedure is discussed in detail. To evaluate the performance of the GA-based SOPNN, the model is experimented with using two time series data (gas furnace and NOx emission process data of gas turbine power plant). A comparative analysis shows that the proposed GA-based SOPNN is model with higher accuracy as well as more superb predictive capability than other intelligent models presented previously.

• 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.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.423-434
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• 2004

In this paper, we introduce a new topology of Self-Organizing Polynomial Neural Networks (SOPNN) based on genetically optimized Multi-Layer Perceptron (MLP) and discuss its comprehensive design methodology involving mechanisms of genetic optimization. Let us recall that the design of the 'conventional' SOPNN uses the extended Group Method of Data Handling (GMDH) technique to exploit polynomials as well as to consider a fixed number of input nodes at polynomial neurons (or nodes) located in each layer. However, this design process does not guarantee that the conventional SOPNN generated through learning results in optimal network architecture. The design procedure applied in the construction of each layer of the SOPNN deals with its structural optimization involving the selection of preferred nodes (or PNs) with specific local characteristics (such as the number of input variables, the order of the polynomials, and input variables) and addresses specific aspects of parametric optimization. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between the approximation and generalization (predictive) abilities of the model. To evaluate the performance of the GA-based SOPNN, the model is experimented using pH neutralization process data as well as sewage treatment process data. A comparative analysis indicates that the proposed SOPNN is the model having higher accuracy as well as more superb predictive capability than other intelligent models presented previously.reviously.