• ETRI Journal
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• 제15권2호
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• pp.35-51
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• 1993

This paper presents function approximation based on nonparametric estimation. As an estimation model of function approximation, a three layered network composed of input, hidden and output layers is considered. The input and output layers have linear activation units while the hidden layer has nonlinear activation units or kernel functions which have the characteristics of bounds and locality. Using this type of network, a many-to-one function is synthesized over the domain of the input space by a number of kernel functions. In this network, we have to estimate the necessary number of kernel functions as well as the parameters associated with kernel functions. For this purpose, a new method of parameter estimation in which linear learning rule is applied between hidden and output layers while nonlinear (piecewise-linear) learning rule is applied between input and hidden layers, is considered. The linear learning rule updates the output weights between hidden and output layers based on the Linear Minimization of Mean Square Error (LMMSE) sense in the space of kernel functions while the nonlinear learning rule updates the parameters of kernel functions based on the gradient of the actual output of network with respect to the parameters (especially, the shape) of kernel functions. This approach of parameter adaptation provides near optimal values of the parameters associated with kernel functions in the sense of minimizing mean square error. As a result, the suggested nonparametric estimation provides an efficient way of function approximation from the view point of the number of kernel functions as well as learning speed.

• 호남수학학술지
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• 제27권2호
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• pp.195-203
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• 2005

We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.

• 대한수학회논문집
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• 제33권2호
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• pp.445-458
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• 2018

In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. Some open problems with this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Bessel-Struve kernel play an important role to derive the main results.

• 한국CDE학회논문집
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• 제6권4호
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• pp.271-276
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• 2001

A geometric kernel is the library of core mathematical functions that defines and stores 3D shapes in response to users'commands. We developed a light geometric kernel suitable to develop CAD/CAM application systems. The kernel contains geometric objects, such as points, curves and surfaces and a minimal set of functions for each type but does not contain lots of modeling and handling functions that are useful to create and maintain complex shapes from an idea sketch. The kernel was developed on MS-Windows NT using C++ with STL(Standard Template Library) but it is compatible with UNIX environments. This paper describes the structure of the kernel including several components: base, math, point sequence curve, geometry, translators. The base kernel gives portability to applications and the math kernel contains basic arithmetic and their classes, such as vector and matrix. The geometry kernel contains points, parametric curves, and parametric surfaces. A neutral fie format and programming and document styles are also presented in this paper.

• 대한수학회보
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• 제37권3호
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• pp.601-618
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• 2000

Let (and $g^*$) be the space of regular test (and generalized, resp.) white noise functions. The integral kernel operators acting on and transformation groups of operators on are studied, and then every integral kernel operator acting on can be extended to continuous linear operator on $g^*$. The existence and uniqueness of solutions of Cauchy problems associated with certain integral kernel operators with intial data in $g^*$ are investigated.

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

• Journal of Information Processing Systems
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• 제15권2호
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• pp.422-432
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• 2019

A hybrid kernel function of support vector machine is proposed to improve the classification performance of power quality disturbances. The kernel function mathematical model of support vector machine directly affects the classification performance. Different types of kernel functions have different generalization ability and learning ability. The single kernel function cannot have better ability both in learning and generalization. To overcome this problem, we propose a hybrid kernel function that is composed of two single kernel functions to improve both the ability in generation and learning. In simulations, we respectively used the single and multiple power quality disturbances to test classification performance of support vector machine algorithm with the proposed hybrid kernel function. Compared with other support vector machine algorithms, the improved support vector machine algorithm has better performance for the classification of power quality signals with single and multiple disturbances.

• 응용통계연구
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• 제24권6호
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• pp.987-994
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• 2011

모집단이 부도와 정상상태로 구분되는 신용평가 관점에서 부도와 정상 상태의 조건부 누적분포함수를 추정하는 방법으로 정규혼합 분포추정과 kernel density estimation을 이용하는 분포추정을 고려한다. 정규혼합 분포의 모수를 EM 알고리즘을 사용해 추정하고, KDE 방법에서는 많이 사용하는 다섯 종류의 커널 함수와 네가지의 띠폭을 이용한다. 그리고 추정한 분포로부터 구한 각각의 ROC 함수를 구한다. 추정한 분포들의 적합도를 비교 분석하고, 이를 바탕으로 구한 ROC 곡선의 성과를 비교 토론한다. 본 연구에서는 KDE 방법으로 추정한 분포함수가 더 적합하고, 추정한 정규혼합 분포를 이용한 ROC 함수가 더 좋은 성과를 나타내는 것을 발견하였다.

• 대한수학회보
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• 제53권5호
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• pp.1291-1308
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• 2016

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids {$z{\in}\mathbb{C}^3:{\mid}z_1{\mid}^p+{\mid}z_2{\mid}^q$ < 1, ${\mid}z_1{\mid}^p+{\mid}z_3{\mid}^r$ < 1}. We consider cases p = 6, q = r = 2 and p = q = r = 2. We also investigate the Lu Qi-Keng problem for p = q = r = 2.

• 한국인터넷방송통신학회논문지
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• 제9권2호
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• pp.1-6
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• 2009

많은 양의 데이터로부터 유용성있는 정보의 추출, 진단 및 예후에 대한 결정, 질병 치료의 응용 등은 바이오 인포머틱스(Bioinformatics)분야에서 매우 중요한 문제들이다. 본 논문에서는 암진단시스템에 적용하기위해 support vector machine을 위한 weogjted lernel fuction과 빠른 수렴성과 좋은 분류성능을 갖는 학습방법을 제안하였다. 제안된 kernel function에서 기본적인 kernel fuction의 weights는 암진단 학습단계에서 결정되고 분류단계에서 파리미터로 사용된다. 대장암 데이터와 같은 임상 데이터에 대한 실험결과에서 제안된 방법은 기존의 다른 kernel fuction들 보다 더 우수하고 안정적인 분류성능을 보여주었다.