• 대한수학회논문집
• /
• 제10권2호
• /
• pp.349-355
• /
• 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 $D \times D$.

• 대한수학회보
• /
• 제58권2호
• /
• pp.515-526
• /
• 2021

Denote by ��+ the set of probability measures supported on ℝ+. Suppose V�� is the variance function of the Cauchy-Stieltjes Kernel (CSK) family ��-(��) generated by a non degenerate probability measure �� ∈ ��+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ${\nu}{\mapsto}{\mathbb{M}}_t({\nu})=({\nu}^{{\boxtimes}(t+1)})^{{\uplus}{\frac{1}{t+1}}}$ from ��+ onto itself.

• 한국지능시스템학회논문지
• /
• 제15권7호
• /
• pp.828-833
• /
• 2005

커널 기법은 데이터를 high dimension 상의 속성 공간으로 mapping함으로써 복잡한 분포를 가지는 데이터에 대하여 기존의 선형 분류 알고리즘들의 성능을 향상시킬 수 있다r4]. 본 논문에서는 기존의 유클리디안 거리측정방법 대신에 커널 함수에 의한 속성 공간의 거리측정방법을 fuzzy K-nearest neighbor(fuzzy K-NN) 알고리즘에 적용한 fuzzy kernel K-nearest neighbor(fuzzy kernel K-NN) 알고리즘을 제안한다. 제시한 알고리즘은 데이터에 대한 적절한 커널 함수의 선택으로 기존 알고리즘의 성능을 향상시킬 수 있다. 제시한 알고리즘의 타당성을 보이기 위하여 여러 데이터 집합에 대한 실험결과와 실제 영상의 분할 결과를 보일 것이다.

• 대한수학회지
• /
• 제47권3호
• /
• pp.537-546
• /
• 2010

Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel function by means of Laplace integral representation of associated Dirichlet series. Using newly derived integral expressions for the Mordell-Tornheim Zeta function a set of subsequent special cases, interesting by themselves, are obtained as corollaries of the main inequality.

• Journal of the Korean Data and Information Science Society
• /
• 제21권1호
• /
• pp.155-162
• /
• 2010

In this paper we propose a doubly penalized kernel method which estimates both the mean function and the variance function simultaneously by kernel machines for heteroscedastic autoregressive data. We also present the model selection method which employs the cross validation techniques for choosing the hyper-parameters which aect the performance of proposed method. Simulated examples are provided to indicate the usefulness of proposed method for the estimation of mean and variance functions.

• Journal of the Korean Data and Information Science Society
• /
• 제24권1호
• /
• pp.201-209
• /
• 2013

For censored regression, it is often the case that some input variables are not important, while some input variables are more important than others. We propose a novel algorithm for selecting such important input variables for censored kernel regression, which is based on the penalized regression with the weighted quadratic loss function for the censored data, where the weight is computed from the empirical survival function of the censoring variable. We employ the weighted version of ANOVA decomposition kernels to choose optimal subset of important input variables. Experimental results are then presented which indicate the performance of the proposed variable selection method.

• Journal of the Korean Data and Information Science Society
• /
• 제25권4호
• /
• pp.951-959
• /
• 2014

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

• 한국전산구조공학회논문집
• /
• 제25권5호
• /
• pp.413-420
• /
• 2012

본 논문은 2차원 선형탄성 직접 경계요소법에서 저매개변수 요소를 사용할 때 Kernel의 적분방법에 대하여 논의하였다. 일반적으로 등매개변수 요소의 경우 형상함수로 통칭되는 해의 기저함수와 요소의 적분을 위해 사용되는 사상함수를 동일하게 사용한다. 그러나 본 논문에서는 사상함수의 차수를 낮게 취하여 순수기저절점을 도입하고 그때 직접 경계요소의 Kernel을 적분하기 위한 방법이 모색되었다. 일반적으로 경계요소법의 적분 Kernel의 경우 Log수치적분과 코쉬주치(Cauchy principal value) 등을 통해 해결하는데, 본 논문에서는 대수적 조작을 통해 적분값의 정확도를 높일 수 있도록 새로운 수식을 유도하였다. 본 연구에서 저매개변수 기반의 직접 경계요소에 대한 강건성과 정확도를 검증하기 위해 2차원 타원형 편미분방정식으로 표현되는 평면응력과 평면변형문제에 대해 적용하였다. 적용 예제로는 단순연결영역(simple connected region)의 대표적 문제인 캔틸레버보와 다중연결영역(multiple connected region)의 대표적인 문제인 개구부가 있는 사각평면에 대해 각각 수치해석을 수행한 결과 대폭적인 자유도의 감소에 비해 정확도 측면에는 기존의 방법과 차이가 없음을 볼 수 있었다. 본 논문에서 제시된 방법은 기저함수 고차화 저매개변수 직접 경계요소법(subparametric high order boundary element)과 이에 기초를 둔 저매개변수 고차 이중경계요소법(subparametric high order dual boundary element)의 초석이 될 수 있을 것이다.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제11권8호
• /
• pp.4043-4060
• /
• 2017

Network Intrusion Detection (NID), an important topic in the field of information security, can be viewed as a pattern recognition problem. The existing pattern recognition methods can achieve a good performance when the number of training samples is large enough. However, modern network attacks are diverse and constantly updated, and the training samples have much smaller size. Furthermore, to improve the learning ability of SVM, the research of kernel functions mainly focus on the selection, construction and improvement of kernel functions. Nonetheless, in practice, there are no theories to solve the problem of the construction of kernel functions perfectly. In this paper, we effectively integrate the advantages of the radial basis function kernel and the polynomial kernel on the notion of the game theory and propose a novel kernel SVM algorithm with game theory for NID, called GTNID-SVM. The basic idea is to exploit the game theory in NID to get a SVM classifier with better learning ability and generalization performance. To the best of our knowledge, GTNID-SVM is the first algorithm that studies ensemble kernel function with game theory in NID. We conduct empirical studies on the DARPA dataset, and the results demonstrate that the proposed approach is feasible and more effective.

• 호남수학학술지
• /
• 제41권1호
• /
• pp.163-174
• /
• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.