• 대한전기학회논문지:시스템및제어부문D
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• 제53권8호
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• pp.551-560
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• 2004

In this paper, we propose a new architecture of Self-Organizing Fuzzy Polynomial Neural Networks (SOFPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially genetic algorithms (GAs). 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. 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, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. 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), A comparative analysis reveals that the proposed SOFPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literatures.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권9호
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 D
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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.

• Journal of Positioning, Navigation, and Timing
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• 제11권4호
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• pp.297-304
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• 2022

The models used for ionosphere error correction in positioning using Global Navigation Satellite System (GNSS) are representatively Klobuchar model and NeQuick model. Although these models can correct the ionosphere error in real time, the disadvantage is that the accuracy is only 50-60%. In this study, a method for polynomial modeling of Global Ionosphere Map (GIM) which provides Vertical Total Electron Content (VTEC) in grid type was studied. In consideration of Ionosphere Pierce Points (IPP) of satellites with a receivable elevation angle of 15 degrees or higher on the Korean Peninsula, the target area for model generation and provision was selected, and the VTEC at 88 GIM grid points was modeled as a polynomial. The developed VTEC polynomial model shows a data reduction rate of 72.7% compared to GIM regardless of the number of visible satellites, and a data reduction rate of more than 90% compared to the Slant Total Electron Content (STEC) polynomial model when there are more than 10 visible satellites. This VTEC polynomial model has a maximum absolute error of 2.4 Total Electron Content Unit (TECU) and a maximum relative error of 9.9% with the actual GIM. Therefore, it is expected that the amount of data can be drastically reduced by providing the predicted GIM or real-time grid type VTEC model as the parameters of the polynomial model.

• 대한전기학회논문지:시스템및제어부문D
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• 제55권2호
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• pp.45-51
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• 2006

In this paper, we propose a new architecture of Information Granulation based genetically optimized Self-Organizing Fuzzy Polynomial Neural Networks (IG_gSOFPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially information granulation and genetic algorithms. The proposed IG_gSOFPNN 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. 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, and a collection of the specific subset of input variables) 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). To evaluate the performance of the IG_gSOFPNN, the model is experimented with using two time series data(gas furnace process and NOx process data).

• 한국컴퓨터그래픽스학회논문지
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• 제6권1호
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• pp.37-50
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• 2000

본 논문에서는 R. T. Farouki에 의하여 소개된 평면 곡선들에 대한 복소수화된 표현법을 사용하여 주어진 임의의 평면 다항식 곡선을 복소수 계수를 갖는 한 다항식으로 나타내고 이 식을 대수학의 기본정리에 따라 복소수체 상에서 완전히 인수분해한 다음 그 근들을 관찰하여 주어진 곡선이 평면 다항식 피타고리안 호도그라프(PH) 곡선이 되기 위하 필요충분 조건을 새로운 방법으로 밝히고, 이를 3차원 민코브스키 공간 $R^{2,1}$ 상의 다항식 곡선에 적용, 이 곡선이 PH 곡선이 되기 위한 필요충분을 보다 간결한 형태로 나타내고 이를 통하여 3차원 민코브스키 공간 $R^{2,1}$ 상의 가능한 다항식 PH 곡선들의 유형이 모두 결정된다는 것을 보인다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.337-339
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• 2004

In this paper, we discuss optimal design of Fuzzy Polynomial Neural Networks by means of Genetic Algorithms(GAs). Proceeding the layer, this model creates the optimal network architecture through the selection and the elimination of nodes by itself. So, there is characteristic of flexibility. We use a triangle and a Gaussian-like membership function in premise part of rules and design the consequent structure by constant and regression polynomial (linear, quadratic and modified quadratic) function between input and output variables. GAs is applied to improve the performance with optimal input variables and number of input variables and order. To evaluate the performance of the GAs-based FPNNs, the models are experimented with the use of Medical Imaging System(MIS) data.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1999년도 하계종합학술대회 논문집
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• pp.741-744
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• 1999

In this paper, We represent a low complexity of parallel canonical basis multiplier for GF( q$^{n}$ ), ( q＞ 2). The Mastrovito multiplier is investigated and applied to multiplication in GF(q$^{n}$ ), GF(q$^{n}$ ) is different with GF(2$^{n}$ ), when MVL is applied to finite field. If q is larger than 2, inverse should be considered. Optimized irreducible polynomial can reduce number of operation. In this paper we describe a method for choosing optimized irreducible polynomial and modularizing recursive polynomial operation. A optimized irreducible polynomial is provided which perform modulo reduction with low complexity. As a result, multiplier for fields GF(q$^{n}$ ) with low gate counts. and low delays are constructed. The architectures are highly modular and thus well suited for VLSI implementation.

• 대한수학회논문집
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• 제31권4호
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• pp.667-682
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• 2016

In this article we show a recursive method to compute the coefficients of the minimal polynomial of cos($2{\pi}/n$) explicitly for $n{\geq}3$. The recursion is not on n but on the coefficient index. Namely, for a given n, we show how to compute ei of the minimal polynomial ${\sum_{i=0}^{d}}(-1)^ie_ix^{d-i}$ for $i{\geq}2$ with initial data $e_0=1$, $e_1={\mu}(n)/2$, where ${\mu}(n)$ is the $M{\ddot{o}}bius$ function.

• 대한원격탐사학회지
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• 제19권5호
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• pp.363-370
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• 2003

This paper describes a rectification procedure that relies on a polynomial model derived from the imaging geometry without loss of accuracy. By using polynomial model, one can effectively eliminate the iterative process to find an image pixel corresponding to each output grid point. With the imaging geometry and ephemeris data, a geo-location polynomial can be constructed from grid points that are produced by solving three equations simultaneously. And, in order to correct the local distortions induced by the geometry and terrain height, a distortion model has been incorporated in the procedure, which is a function of incidence angle and height at each pixel position. With this function, it is straightforward to calculate the pixel displacement due to distortions and then pixels are assigned to the output grid by re-sampling the displaced pixels. Most of the necessary information for the construction of polynomial model is available in the leader file and some can be derived from others. For validation, sample images of ERS-l PRI and Radarsat-l SGF have been processed by the proposed method and evaluated against ground truth acquired from 1:25,000 topography maps.