• Interaction and multiscale mechanics
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• v.3 no.3
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• pp.277-298
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• 2010

The complex variable reproducing kernel particle method (CVRKPM) and the FEM are coupled in this paper to analyze the two-dimensional potential problems. The coupled method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, resulting in improved computational efficiency. A hybrid approximation function is applied to combine the CVRKPM with the FEM. Formulations of the coupled method are presented in detail. Three numerical examples of the two-dimensional potential problems are presented to demonstrate the effectiveness of the new method.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.115-124
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• 2014

In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.227-232
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• 2003

Recently, support vector learning attracts an enormous amount of interest in the areas of function approximation, pattern classification, and novelty detection. One of the main reasons for the success of the support vector machines(SVMs) seems to be the availability of global and sparse solutions. Among the approaches sharing the same reasons for success and exhibiting a similarly good performance, we have KFD(kernel Fisher discriminant) approach. In this paper, we consider the problem of function approximation utilizing both predetermined basis functions and the KFD approach for regression. After reviewing support vector regression, semi-parametric approach for including predetermined basis functions, and the KFD regression, this paper presents an extension of the conventional KFD approach for regression toward the direction that can utilize predetermined basis functions. The applicability of the presented method is illustrated via a regression example.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.297-305
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• 2008

Recently, kernel methods have attracted great interests in the areas of pattern classification, function approximation, and anomaly detection. The role of the kernel is particularly important in the methods such as SVM(support vector machine) and KPCA(kernel principal component analysis), for it can generalize the conventional linear machines to be capable of efficiently handling nonlinearities. This paper considers the problem of combining radar and rain gauge observations utilizing the regression approach based on the kernel-based gaussian process and support vector learning. The data-assimilation results of the considered methods are reported for the radar and rain gauge observations collected over the region covering parts of Gangwon, Kyungbuk, and Chungbuk provinces of Korea, along with performance comparison.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.19-38
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• 2006

We analyze the spectral collocation approximation for a parabolic partial integrodifferential equations(PIDE) with a weakly singular kernel. The space discretization is based on the spectral collocation method and the time discretization is based on Crank-Nicolson scheme with a graded mesh. We obtain the stability and second order convergence result for fully discrete scheme.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.349-355
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• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.337-347
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• 2024

Kernel density estimation is a prevalent technique employed for nonparametric density estimation, enabling direct estimation from the data itself. This estimation involves two crucial elements: selection of the kernel function and the determination of the appropriate bandwidth. The selection of the bandwidth plays an important role in kernel density estimation, which has been developed over the past decade. A range of methods is available for selecting the bandwidth, including the plug-in bandwidth. In this article, the proposed plug-in bandwidth is introduced, which leverages shifted Chebyshev series-based approximation to determine the optimal bandwidth. Through a simulation study, the performance of the suggested bandwidth is analyzed to reveal its favorable performance across a wide range of distributions and sample sizes compared to alternative bandwidths. The proposed bandwidth is also applied for kernel density estimation on real dataset. The outcomes obtained from the proposed bandwidth indicate a favorable selection. Hence, this article serves as motivation to explore additional plug-in bandwidths that rely on function approximations utilizing alternative series expansions.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.607-617
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• 2003

This paper offers a practical comparison of efficiency between local likelihood approach and conventional kernel approach in density estimation. The local likelihood estimation procedure maximizes a kernel smoothed log-likelihood function with respect to a polynomial approximation of the log likelihood function. We use two types of data driven bandwidths for each method and compare the mean integrated squares for several densities. Numerical results reveal that local log-linear approach with simple plug-in bandwidth shows better performance comparing to the standard kernel approach in heavy tailed distribution. For normal mixture density cases, standard kernel estimator with the bandwidth in Sheather and Jones(1991) dominates the others in moderately large sample size.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.671-690
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• 2004

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2019.06a
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• pp.84-85
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• 2019

MPEG-NNR (Compression of Neural Network for Multimedia Content Description and Analysis) aims to define a compressed and interoperable representation of trained neural networks. In this paper, we present a low-rank approximation to compress a CNN used for image compression, which is one of MPEG-NNR use cases. In the presented method, the low-rank approximation decomposes one 2D kernel matrix of weights into two 1D kernel matrix values in each convolution layer to reduce the data amount of weights. The evaluation results show that the model size of the original CNN is reduced to half as well as the inference runtime is reduced up to about 30% with negligible loss in PSNR.