• 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.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.12-14
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• 2005

In this paper, we propose a new architecture of Self-Organizing Fuzzy Polynomial Neural Networks(SOFPNN) by means of genetically optimized fuzzy polynomial neuron(FPN) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially genetic algorithms(GAs). The conventional SOFPNNs hinges on an extended Group Method of Data Handling(GMDH) and exploits a fixed fuzzy inference type in each FPN of the SOFPNN as well as considers a fixed number of input nodes located in each layer. The design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics (such as the number of input variables, the order of the polynomial of the consequent part of fuzzy rules, a collection of the specific subset of input variables, and the number of membership function) and addresses specific aspects of parametric optimization. Therefore, the proposed SOFPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional SOFPNNs. To evaluate the performance of the genetically optimized SOFPNN, the model is experimented with using two time series data(gas furnace and chaotic time series).

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.6
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• pp.264-273
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• 2006

In this paper, we propose a new architecture of Self-Organizing Fuzzy Polynomial Neural Networks (SOFPNN) by means of consecutive optimization and also discuss its comprehensive design methodology involving mechanisms of genetic optimization. The network is based on a structurally as well as parametrically optimized fuzzy polynomial neurons (FPNs) conducted with the aid of information granulation and genetic algorithms. In structurally identification of FPN, the design procedure applied in the construction of each layer of a SOFPNN deals with its structural optimization involving the selection of preferred nodes (or FPNs) with specific local characteristics and addresses specific aspects of parametric optimization. In addition, the fuzzy rules used in the networks exploit the notion of information granules defined over system's variables and formed through the process of information granulation. That is, we determine the initial location (apexes) of membership functions and initial values of polynomial function being used in the premised and consequence part of the fuzzy rules respectively. This granulation is realized with the aid of the hard c-menas clustering method (HCM). For the parametric identification, we obtained the effective model that the axes of MFs are identified by GA to reflect characteristic of given data. Especially, the genetically dynamic search method is introduced in the identification of parameter. It helps lead to rapidly optimal convergence over a limited region or a boundary condition. To evaluate the performance of the proposed model, the model is experimented with using two time series data(gas furnace process, nonlinear system data, and NOx process data).

• Journal of Electrical Engineering and Technology
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• v.12 no.2
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• pp.911-917
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• 2017

There are generally three folds when developing neural network classifiers. They are as follows: 1) discriminant function; 2) lots of parameters in the design of classifier; and 3) high dimensional training data. Along with this viewpoint, we propose space search optimized polynomial neural network classifier (PNNC) with the aid of data preprocessing technique and simultaneous tuning strategy, which is a balance optimization strategy used in the design of PNNC when running space search optimization. Unlike the conventional probabilistic neural network classifier, the proposed neural network classifier adopts two type of polynomials for developing discriminant functions. The overall optimization of PNNC is realized with the aid of so-called structure optimization and parameter optimization with the use of simultaneous tuning strategy. Space search optimization algorithm is considered as a optimize vehicle to help the implement both structure and parameter optimization in the construction of PNNC. Furthermore, principal component analysis and linear discriminate analysis are selected as the data preprocessing techniques for PNNC. Experimental results show that the proposed neural network classifier obtains better performance in comparison with some other well-known classifiers in terms of accuracy classification rate.

• 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.

• Journal of Power System Engineering
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• v.21 no.5
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• pp.41-47
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• 2017

To implement Argentina tango dancer-like walking of the humanoid robot, a new trajectory generation scheme based on particle swarm optimization of the blending polynomial is presented. Firstly, the characteristics of Argentina tango walking are derived from observation of tango dance. Secondly, these are reflected in walking pose conditions and cost functions of particle swarm optimization to determine the coefficients of blending polynomial. For the stability of biped walking, zero moment point and reference trajectory of swing foot are also included in cost function. Thirdly, after tango walking cycle is divided into 3 stages with 2 postures, optimal trajectories of ankles, knees and hip of lower body, which include 6 sagittal and 4 coronal angles, are derived in consequence of optimization. Finally, the feasibility of the proposed scheme is validated by simulating biped walking of humanoid robot with derived trajectories under the 3D Simscape environment.

• Journal of Electrical Engineering and Technology
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• v.13 no.4
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• pp.1724-1731
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• 2018

The conventional polynomial neural network (PNN) is a classical flexible neural structure and self-organizing network, however it is not free from the limitation of overfitting problem. In this study, we propose a space search-optimized polynomial neural network (ssPNN) structure to alleviate this problem. Ranking selection is realized by means of ranking selection-based performance index (RS_PI) which is combined with conventional performance index (PI) and coefficients based performance index (CPI) (viz. the sum of squared coefficient). Unlike the conventional PNN, L2-norm regularization method for estimating the polynomial coefficients is also used when designing the ssPNN. Furthermore, space search optimization (SSO) is exploited here to optimize the parameters of ssPNN (viz. the number of input variables, which variables will be selected as input variables, and the type of polynomial). Experimental results show that the proposed ranking selection-based polynomial neural network gives rise to better performance in comparison with the neuron fuzzy models reported in the literatures.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2888-2890
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• 2005

In this paper, we introduce a new structure of fuzzy-neural networks Fuzzy Set-based Polynomial Neural Networks (FSPNN). The two underlying design mechanisms of such networks involve genetic optimization and information granulation. The resulting constructs are Fuzzy Polynomial Neural Networks (FPNN) with fuzzy set-based polynomial neurons (FSPNs) regarded as their generic processing elements. First, we introduce a comprehensive design methodology (viz. a genetic optimization using Genetic Algorithms) to determine the optimal structure of the FSPNNs. This methodology hinges on the extended Group Method of Data Handling (GMDH) and fuzzy set-based rules. It concerns FSPNN-related parameters such as the number of input variables, the order of the polynomial, the number of membership functions, and a collection of a specific subset of input variables realized through the mechanism of genetic optimization. Second, the fuzzy rules used in the networks exploit the notion of information granules defined over systems variables and formed through the process of information granulation. This granulation is realized with the aid of the hard C- Means clustering (HCM). The performance of the network is quantified through experimentation in which we use a number of modeling benchmarks already experimented with in the realm of fuzzy or neurofuzzy modeling.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.651-654
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• 2008

In finite field operations based on $GF(2^m)$, additions and subtractions are easily implemented. On the other hand, multiplications and divisions require mathematical elaboration of complex equations. There are two dominant way of approaching the solutions of finite filed operations, normal basis approach and polynomial basis approach, each of which has both benefits and weakness respectively. In this study, we adopted the mathematically feasible polynomial basis approach and suggest the optimization techniques of finite field operations based of mathematical principles.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.33-38
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• 2006

In this paper, we propose a new architecture of Fuzzy Polynomial Neural Networks(FPNN) by means of genetically optimized Fuzzy Polynomial Neuron(FPN) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially Genetic Algorithms(GAs). The conventional FPNN developed so far are based on mechanisms of self-organization and evolutionary optimization. The design of the network exploits the extended Group Method of Data Handling(GMDH) with some essential parameters of the network being provided by the designer and kept fixed throughout the overall development process. This restriction may hamper a possibility of producing an optimal architecture of the model. The proposed FPNN gives rise to a structurally optimized network and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. It is shown that the proposed advanced genetic algorithms based Fuzzy Polynomial Neural Networks is more useful and effective than the existing models for nonlinear process. We experimented with Medical Imaging System(MIS) dataset to evaluate the performance of the proposed model.