• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.3
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• pp.135-144
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• 2004

In this paper, we propose competitive fuzzy polynomial neurons-based advanced Self-Organizing Neural Networks(SONN) architecture for optimal model identification and discuss a comprehensive design methodology supporting its development. The proposed SONN dwells on the ideas of fuzzy rule-based computing and neural networks. And it consists of layers with activation nodes based on fuzzy inference rules and regression polynomial. Each activation node is presented as Fuzzy Polynomial Neuron(FPN) which includes either the simplified or regression polynomial fuzzy inference rules. As the form of the conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership (unction are studied and the number of the premise input variables used in the rules depends on that of the inputs of its node in each layer. We introduce two kinds of SONN architectures, that is, the basic and modified one with both the generic and the advanced type. Here the basic and modified architecture depend on the number of input variables and the order of polynomial in each layer. The number of the layers and the nodes in each layer of the SONN are not predetermined, unlike in the case of the popular multi-layer perceptron structure, but these are generated in a dynamic way. The superiority and effectiveness of the Proposed SONN architecture is demonstrated through two representative numerical examples.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.4
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• pp.110-118
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• 1997

Multi-layer neural networks with error back-propagation algorithm have a great potential for identifying nonlinear systems with unknown characteristics. However, because they have a demerit that the speed of convergence is too slow, various methods for improving the training characteristics of backpropagition networks have been proposed. In this paper, a fuzzy division method is proposed to improve the convergence speed, which can find out an effective fuzzy division by the tuning of membership function and independently train each neural network after dividing the network model into several parts. In the simulations, the proposed method showed that the optimal fuzzy partitions could be found from the arbitray initial ones and that the convergence speed was faster than the traditional method without the fuzzy division.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.4
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• pp.534-540
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• 2014

In this paper, we propose a fuzzy combined Polynomial Neural Network(PNN) for pattern classification. The fuzzy combined PNN comes from the generic TSK fuzzy model with several linear polynomial as the consequent part and is the expanded version of the fuzzy model. The proposed pattern classifier has the polynomial neural networks as the consequent part, instead of the general linear polynomial. PNNs are implemented by stacking the simple polynomials dynamically. To implement one layer of PNNs, the various types of simple polynomials are used so that PNNs have flexibility and versatility. Although the structural complexity of the implemented PNNs is high, the PNNs become a high order-multi input polynomial finally. To estimate the coefficients of a polynomial neuron, The weighted linear discriminant analysis. The output of fuzzy rule system with PNNs as the consequent part is the linear combination of the output of several PNNs. To evaluate the classification ability of the proposed pattern classifier, we make some experiments with several machine learning data sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.2
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• pp.236-244
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• 2005

In this study, we introduce a new topology of Fuzzy Polynomial Neural Networks(FPNN) that is based on fuzzy relation and evolutionally optimized Multi-Layer Perceptron, discuss a comprehensive design methodology and carry out a series of numeric experiments. The construction of the evolutionally optimized FPNN(EFPNN) exploits fundamental technologies of Computational Intelligence. The architecture of the resulting EFPNN results from a synergistic usage of the genetic optimization-driven hybrid system generated by combining rule-based Fuzzy Neural Networks(FNN) with polynomial neural networks(PNN). FNN contributes to the formation of the premise part of the overall rule-based structure of the EFPNN. The consequence part of the EFPNN is designed using PNN. As the consequence part of the EFPNN, the development of the genetically optimized PNN(gPNN) dwells on two general optimization mechanism: the structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the EFPNN, the models are experimented with the use of several representative numerical examples. A comparative analysis shows that the proposed EFPNN are models with higher accuracy as well as more superb predictive capability than other intelligent models presented previously.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.52-58
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• 2005

We have developed a Group Method of Data Handling (GMDH) type algorithm for designing multi-layered neural networks. The algorithm is general enough that it will accept any number of inputs and any sized training set. Each neuron of the resulting network is a function of two of the inputs to the layer. The equation for each of the neurons is a quadratic polynomial. Several forms of the equation are tested for each neuron to make sure that only the best equation of two inputs is kept. All possible combinations of two inputs to each layer are also tested. By carefully testing each resulting neuron, we have developed an algorithm to keep only the best neurons at each level. The algorithm's goal is to create as accurate a network as possible while minimizing the size of the network. Software was developed to train and simulate networks using our algorithm. Several applications were modeled using our software, and the result was that our algorithm succeeded in developing small, accurate, multi-layer networks.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.675-677
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• 1998

In this paper, we propose the fuzzy inference algorithm with multi-layer structure. MFIS(Multi-layer Fuzzy Inference System) uses PNN(Polynomial Neural networks) structure and the fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Hendling), and uses several types of polynomials such as linear, quadratic and cubic, as well as the biquadratic polynomial used in the GMDH. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here, the regression polynomial inference is based on consequence of fuzzy rules with the polynomial equations such as linear, quadratic and cubic equation. Each node of the MFIS is defined as fuzzy rules and its structure is a kind of neuro-fuzzy structure. We use the training and testing data set to obtain a balance between the approximation and the generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2856-2858
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• 1999

In this paper, the FPNN(Fuzzy Polynomial Neural Networks) algorithm with multi-layer fuzzy inference structure is proposed for the model identification of a complex nonlinear system. The FPNN structure is generated from the mutual combination of PNN (Polynomial Neural Network) structure and fuzzy inference method. The PNN extended from the GMDH(Group Method of Data Handling) uses several types of polynomials such as linear, quadratic and modifled quadratic besides the biquadratic polynomial used in the GMDH. In the fuzzy inference method, simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used Each node of the FPNN is defined as a fuzzy rule and its structure is a kind of fuzzy-neural networks. Gas furnace data used to evaluate the performance of our proposed model.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1017-1020
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• 1993

This paper describes a neo fuzzy neuron which was produced by a fusion of fuzzy logic and neuroscience. Some learning algorithms are presented. The guarantee for the global minimum on the error-weight space is proved by a reduction to absurdity. Enhanced is that the learning speed of the neo fuzzy neuron exceeds 100,000 times of that of conventional multi-layer neural networks.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.2
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• pp.312-320
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• 2012

In this study, we introduce a new design methodology of a granular-oriented self-organizing polynomial neural networks (GoSOPNNs) 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 methodological design strategy of GoSOPNNs as follows : (a) The 1st layer of the proposed network consists of Context-based Polynomial Neuron (CPN). In 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 while the build of the clusters is guided by a collection of some predefined fuzzy sets (so-called contexts) defined in the output space. (b) The proposed design procedure being applied at each layer of GoSOPNN leads to the selection of 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 performance of the proposed GoSOPNN network, we describe a detailed characteristic of the proposed model using a well-known learning machine data(Automobile Miles Per Gallon Data, Boston Housing Data, Medical Image System Data).

• 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.