• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.1863_1864
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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 입력개수, 입력변수, 클러스터의 개수를 PSO알고리즘(Particle Swarm Optimization)을 사용하여 최적화 시켰다. 제안한 모델의 적용 및 유용성을 비교 평가하기 위하여 비선형 데이터를 이용하여 그 우수성을 보인다.

• ETRI Journal
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• v.26 no.4
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• pp.297-306
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• 2004

A plasma is a collection of charged particles and on average is electrically neutral. In fabricating integrated circuits, plasma etching is a key means to transfer a photoresist pattern into an underlayer material. To construct a predictive model of plasma-etching processes, a polynomial neural network (PNN) is applied. This process was characterized by a full factorial experiment, and two attributes modeled are its etch rate and DC bias. According to the number of input variables and type of polynomials to each node, the prediction performance of the PNN was optimized. The various performances of the PNN in diverse environments were compared to three types of statistical regression models and the adaptive network fuzzy inference system (ANFIS). As the demonstrated high-prediction ability in the simulation results shows, the PNN is efficient and much more accurate from the point of view of approximation and prediction abilities.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2876-2878
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• 2005

In this paper, we propose Genetic Algorithms(GAs)-based Optimal Polynomial Neural Networks(PNN). The proposed algorithm is based on Group Method of Data Handling(GMDH) method and its structure is similar to feedforward Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and can be generated. The each node of PNN structure uses several types of high-order polynomial such as linear, quadratic and modified quadratic, and is connected as various kinds of multi-variable inputs. The conventional PNN depends on experience of a designer that select No. of input variable, input variable and polynomial type. Therefore it is very difficult a organizing of optimized network. The proposed algorithm identified and selected No. of input variable, input variable and polynomial type by using Genetic Algorithms(GAs). In the sequel the proposed model shows not only superior results to the existing models, but also pliability in organizing of optimal network. The study is illustrated with the ACI Distance Relay Data for application to power systems.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1964-1965
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• 2011

본 연구에서는 패턴분류를 위해 기존의 방사형 기저 함수 신경회로망(Radial Basis Funtion Neural Network)과 다항식 신경회로망(Polynomial Neural Network)을 결합한 다중 출력 방사형 기저 함수다항식 신경회로망 (Multi Output Radial Basis Funtion Polynomial Neural Network)의 분류기를 제안한다. 제안된 모델은 PNN을 기본 구조로 하여 1층에 기존의 다항식 노드 대신 다중 출력 형태의 RBFNN을 적용 한다. RBFNN의 은닉층에는 기존의 활성함수가 아닌 fuzzy 클러스터링을 사용하여 입력 데이터의 특성을 고려한 적합도를 사용하였다. PNN은 입력변수의 수와 다항식 차수가 모델의 성능을 결정함으로 최적화가 필요하며 본 논문에서는 Differential Evolution(DE)을 사용하여 모델의 구조 및 파라미터를 최적화시켜 모델의 성능을 향상시켰다. 패턴분류기로써의 제안된 모델을 평가하기 위해 pima 데이터를 이용하였다.

• International Journal of Control, Automation, and Systems
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• v.1 no.3
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• pp.321-331
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• 2003

Experimental software datasets describing software projects in terms of their complexity and development time have been the subject of intensive modeling. A number of various modeling methodologies and modeling designs have been proposed including such approaches as neural networks, fuzzy, and fuzzy neural network models. In this study, we introduce the concept of the Rule-based fuzzy polynomial neural networks (RFPNN) as a hybrid modeling architecture and discuss its comprehensive design methodology. The development of the RFPNN dwells on the technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The architecture of the RFPNN results from a synergistic usage of RFNN and PNN. RFNN contribute to the formation of the premise part of the rule-based structure of the RFPNN. The consequence part of the RFPNN is designed using PNN. We discuss two kinds of RFPNN architectures and propose a comprehensive learning algorithm. In particular, it is shown that this network exhibits a dynamic structure. The experimental results include well-known software data such as the NASA dataset concerning software cost estimation and the one describing software modules of the Medical Imaging System (MIS).

• 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.66 no.12
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• pp.1772-1781
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• 2017

In this study, the design methodology for alleviating the overfitting problem of Polynomial Neural Networks(PNN) is realized with the aid of two kinds techniques such as L2 regularization and Sum of Squared Coefficients (SSC). The PNN is widely used as a kind of mathematical modeling methods such as the identification of linear system by input/output data and the regression analysis modeling method for prediction problem. PNN is an algorithm that obtains preferred network structure by generating consecutive layers as well as nodes by using a multivariate polynomial subexpression. It has much fewer nodes and more flexible adaptability than existing neural network algorithms. However, such algorithms lead to overfitting problems due to noise sensitivity as well as excessive trainning while generation of successive network layers. To alleviate such overfitting problem and also effectively design its ensuing deep network structure, two techniques are introduced. That is we use the two techniques of both SSC(Sum of Squared Coefficients) and $L_2$ regularization for consecutive generation of each layer's nodes as well as each layer in order to construct the deep PNN structure. The technique of $L_2$ regularization is used for the minimum coefficient estimation by adding penalty term to cost function. $L_2$ regularization is a kind of representative methods of reducing the influence of noise by flattening the solution space and also lessening coefficient size. The technique for the SSC is implemented for the minimization of Sum of Squared Coefficients of polynomial instead of using the square of errors. In the sequel, the overfitting problem of the deep PNN structure is stabilized by the proposed method. This study leads to the possibility of deep network structure design as well as big data processing and also the superiority of the network performance through experiments is shown.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.483-487
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• 2005

We introduce a new architecture of hetero-hybridized feed-forward neural networks composed of fuzzy set-based polynomial neural networks (FSPNN) and polynomial neural networks (PM) that are based on a genetically optimized multi-layer perceptron and develop their comprehensive design methodology involving mechanisms of genetic optimization and Information Granulation. The construction of Information Granulation based HFSPNN (IG-HFSPNN) exploits fundamental technologies of Computational Intelligence(Cl), namely fuzzy sets, neural networks, and genetic algorithms(GAs) and Information Granulation. The architecture of the resulting genetically optimized Information Granulation based HFSPNN (namely IG-gHFSPNN) results from a synergistic usage of the hybrid system generated by combining new fuzzy set based polynomial neurons (FPNs)-based Fuzzy Neural Networks(PM) with polynomial neurons (PNs)-based Polynomial Neural Networks(PM). The design of the conventional genetically optimized HFPNN exploits the extended Group Method of Data Handling(GMDH) with some essential parameters of the network being tuned by using Genetie Algorithms throughout the overall development process. However, the new proposed IG-HFSPNN adopts a new method called as Information Granulation to deal with Information Granules which are included in the real system, and a new type of fuzzy polynomial neuron called as fuzzy set based polynomial neuron. The performance of the IG-gHFPNN is quantified through experimentation.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.701-712
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• 2009

In this paper, we study the simultaneous approximation to functions in $C^m$[0, 1] by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1386-1388
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• 1996

In this paper, a recurrent neural network using polynomial is proposed for electric load forecasting. Since the proposed algorithm is based on the bilinear polynomial, it can model nonlinear systems with much more parsimony than the higher order neural networks based on the Volterra series. The proposed Bilinear Recurrent Neural Network(BLRNN) is compared with Multilayer Perceptron Type Neural Network(MLPNN) for electric load forecasting problems. The results show that the BLRNN is robust and outperforms the MLPNN in terms of forecasting accuracy.