• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.849-854
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• 1995

The interpolation of scattered data with radial basis functions is knwon for its good fitting. But if data get large, the coefficient matrix becomes almost singular. We introduce different knots and nodes to improve condition number of coefficient matrix. The singulaity of new coefficient matrix is investigated here.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.1
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• pp.128-135
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• 2015

In this study, we develop the very short-term precipitation forecasting model as well as classifier based on polynomial radial basis function neural networks by using AWS(Automatic Weather Station) and KLAPS(Korea Local Analysis and Prediction System) meteorological data. The polynomial-based radial basis function neural networks is designed to realize precipitation forecasting model as well as classifier. The structure of the proposed RBFNNs consists of three modules such as condition, conclusion, and inference phase. The input space of the condition phase is divided by using Fuzzy C-means(FCM) and the local area of the conclusion phase is represented as four types of polynomial functions. The coefficients of connection weights are estimated by weighted least square estimation(WLSE) for modeling as well as least square estimation(LSE) method for classifier. The final output of the inference phase is obtained through fuzzy inference method. The essential parameters of the proposed model and classifier such ad input variable, polynomial order type, the number of rules, and fuzzification coefficient are optimized by means of Particle Swarm Optimization(PSO) and Differential Evolution(DE). The performance of the proposed precipitation forecasting system is evaluated by using KLAPS meteorological data.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.1 no.3
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• pp.69-76
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• 2008

This paper concerns Fuzzy Radial Basis Function Neural Network (FRBFNN) and automatic rule generation of extraction of the FRBFNN by means of mountain clustering. In the proposed network, the membership functions of the premise part of fuzzy rules do not assume any explicit functional forms such as Gaussian, ellipsoidal, triangular, etc., so its resulting fitness values (degree of membership) directly rely on the computation of the relevant distance between data points. Also, we consider high-order polynomial as the consequent part of fuzzy rules which represent input-output characteristic of sup-space. The number of clusters and the centers of clusters are automatically generated by using mountain clustering method based on the density of data. The centers of cluster which are obtained by using mountain clustering are used to determine a degree of membership and weighted least square estimator (WLSE) is adopted to estimate the coefficients of the consequent polynomial of fuzzy rules. The effectiveness of the proposed model have been investigated and analyzed in detail for the representative nonlinear function.

• Bulletin of the Korean Chemical Society
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• v.6 no.5
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• pp.264-266
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• 1985

Orthogonalized Slater-type orbitals and Ortho-normalized Slater-type orbitals were derived from the conventional Slater-type orbitals (STO's) by use of the continuous orthonormalizing which is expanded from the Schmidt's orthogonalizing procedure. These orbitals have the merits which STO's have not, such as; they are ortho-normalized each other and have the same numbers of the radial nodes that the real hydrogenlike wave functions do, so that they must be a good basis functions of LCAO MO procedures, i.e., the best approximate representation of SCF method.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.4
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• pp.74-81
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• 1997

This paper proposes an evolutionary learning algorithm to discipline the projection neural nctworks (PNNs) with special type of hidden nodes which can activate radial basis functions as well as sigmoid functions. The proposed algorithm not only trains the parameters and the connection weights hut also c~ptimizes the network structure. Through the structure optimization, the number of hidden node:; necessary to represent a given target function is determined and the role of each hidden node is decided whether it activates a radial basis function or a sigmoid function. To apply the algorithm, PNN is realized by a self-organizing genotype representation with a linked list data structure. Simulations show that the algorithm can build the PNN with less hidden nodes than thc existing learning algorithm using error hack propagation(EE3P) and network growing strategy.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.709-720
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• 2017

In healthcare and medical research, many important variables have a measurement error such as body mass index and laboratory data. It is also not easy to collect samples of large size because of high cost and long time required to collect the target patient satisfied with inclusion and exclusion criteria. Beside, the demand for solving a complex scientific problem has highly increased so that a semiparametric regression approach could be of substantial value solving this problem. To address the issues of measurement error, small domain and a scientific complexity, we conduct a multivariable Bayesian smoothing under structural measurement error covariate in this article. Specifically we enhance our previous model by incorporating other useful auxiliary covariates free of measurement error. For the regression spline, we use a radial basis functions with fixed knots for the measurement error covariate. We organize a fully Bayesian approach to fit the model and estimate parameters using Markov chain Monte Carlo. Simulation results represent that the method performs well. We illustrate the results using a national survey data for application.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.365-376
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• 2004

The purpose of this study is to show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met. In particular, as a basis function, we are interested in using a conditionally positive definite function $\Phi$ whose generalized Fourier transform is of the form $\Phi(\theta)\;=\;F(\theta)$\mid$\theta$\mid$^{-2m}$ with a bounded function F > 0.

• Journal of Computing Science and Engineering
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• v.2 no.1
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• pp.98-108
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• 2008

Terrain reconstruction from images is an ill-posed, yet commonly desired Structure from Motion task when compositing visual effects into live-action photography. These surfaces are required for choreography of a scene, casting physically accurate shadows of CG elements, and occlusions. We present a novel framework for generating the geometry of landscapes from extremely noisy point cloud datasets obtained via limited resolution techniques, particularly optical flow based vision algorithms applied to live-action video plates. Our contribution is a new statistical approach to remove erroneous tracks ('outliers') by employing a unique combination of well established techniques-including Gaussian Mixture Models (GMMs) for robust parameter estimation and Radial Basis Functions (REFs) for scattered data interpolation-to exploit the natural constraints of this problem. Our algorithm offsets the tremendously laborious task of modeling these landscapes by hand, automatically generating a visually consistent, camera position dependent, thin-shell surface mesh within seconds for a typical tracking shot.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.163.1-163
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• 2001

In this paper, we use time-frequency localization analysis method to analize the target function and the area of the target space. When we analize the function with the time and frequency axis simultaneously, the characteristic of the function is shown more precisely and the area is covered by a certain block. After we analize the target function in the time-frequency space, we can decide the activation functions and compose the hidden layer of the RBFN by choosing the radial basis function which can represent the characteristic of the target function, RBFN made by this method, designs the good structure proper to the target problem because we can decide the number of hidden node first.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1650-1653
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• 2002

In this paper, we propose the initial optimized structure of the Radial Basis function Networks that is simple in the part of the structure and fast converges more than neural networks with the analysis method using Time- Frequency Localization. We construct the hidden node with the Radial Basis functions their localization are similar with approximation target function in the plane of the Time and Frequency. We finally make a good decision of the initial structure for function approximation using genetic algorithm