• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권3호
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• pp.199-208
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• 2019

A necessary and sufficient condition in terms of lower cut sets is given for the insertion of a Baire-.5 function between two comparable real-valued functions on the topological spaces that whose $F_{\sigma}$-kernel of sets are $F_{\sigma}$-sets.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권1호
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• pp.1-12
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• 2019

Necessary and sufficient conditions in terms of lower cut sets are given for the strong insertion of a Baire-.5 function between two comparable real-valued functions on the topological spaces that $F_{\sigma}-kernel$ of sets are $F_{\sigma}-sets$.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2001년도 추계학술대회 학술발표 논문집
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• pp.60-64
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• 2001

In this paper, a new learning methodology for Kernel Methods is suggested that results in a sparse representation of kernel space from the training patterns for classification problems. Among the traditional algorithms of linear discriminant function(perceptron, relaxation, LMS(least mean squared), pseudoinverse), this paper shows that the relaxation procedure can obtain the maximum margin separating hyperplane of linearly separable pattern classification problem as SVM(Support Vector Machine) classifier does. The original relaxation method gives only the necessary condition of SV patterns. We suggest the sufficient condition to identify the SV patterns in the learning epochs. Experiment results show the new methods have the higher or equivalent performance compared to the conventional approach.

• 한국해안·해양공학회논문집
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• 제24권1호
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• pp.1-9
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• 2012

조위편차는 최근 기후변화에 의한 영향으로 연안 안전 방재 측면에서 매우 중요한 인자로 부각되고 있다. 태풍강도 등과 더불어 변화가 예상되는 조위편차는 해안구조물의 안전 및 기능검토에 필요한 기준해수면 결정에 기여하는 중요한 인자이다. 우리나라 연안 조위편차의 확률밀도함수는 음 양의 왜도와 정규분포보다 큰 돌도를 가지는 분포로, 정규분포로 근사화하는 방법은 한계가 있기 때문에 본 연구에서는 비모수적 방법인 Kernel 함수를 이용하여 확률밀도함수를 추정 제안하였다. 본 연구에서 제안된 확률밀도함수는 조위편차자료의 분포와 매우 우수한 일치수준을 보이고 있으며, 다양한 극값 추정에도 높은 수준의 정도를 보여주고 있다.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1419-1427
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• 2008

This paper shows the kernel Poisson regression which can be applied in the claims reserving, where the row effect is assumed to be a nonlinear function of the row index. The paper concentrates on the chain-ladder technique, within the framework of the chain-ladder linear model. It is shown that the proposed method can provide better reserve estimates than the Poisson model. The cross validation function is introduced to choose optimal hyper-parameters in the procedure. Experimental results are then presented which indicate the performance of the proposed model.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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• pp.735-744
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• 2007

Support vector machine(SVM) is capable of providing a more complete description of the linear and nonlinear relationships among random variables. In this paper we propose a sparse kernel regression(SKR) to overcome a weak point of SVM, which is, the steep growth of the number of support vectors with increasing the number of training data. The iterative reweighted least squares(IRWLS) procedure is used to solve the optimal problem of SKR with a Laplacian prior. Furthermore, the generalized cross validation(GCV) function is introduced to select the hyper-parameters which affect the performance of SKR. Experimental results are then presented which illustrate the performance of the proposed procedure.

• 대한수학회지
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• 제53권6호
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• pp.1431-1443
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• 2016

Let k be a global field of characteristic unequal to two. Let $C:y^2=f(x)$ be a nonsingular projective curve over k, where f(x) is a quartic polynomial over k with nonzero discriminant, and K = k(C) be the function field of C. For each prime spot p on k, let ${\hat{k}}_p$ denote the corresponding completion of k and ${\hat{k}}_p(C)$ the function field of $C{\times}_k{\hat{k}}_p$. Consider the map $$h:Br(K){\rightarrow}{\prod\limits_{\mathfrak{p}}}Br({\hat{k}}_p(C))$$, where p ranges over all the prime spots of k. In this paper, we explicitly describe all the constant classes (coming from Br(k)) lying in the kernel of the map h, which is an obstruction to the Hasse principle for the Brauer groups of the curve. The kernel of h can be expressed in terms of quaternion algebras with their prime spots. We also provide specific examples over ${\mathbb{Q}}$, the rationals, for this kernel.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권2호
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• pp.702-723
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• 2020

The application of machine learning (ML) in intrusion detection has attracted much attention with the rapid growth of information security threat. As an efficient multi-label classifier, kernel extreme learning machine (KELM) has been gradually used in intrusion detection system. However, the performance of KELM heavily relies on the kernel selection. In this paper, a novel multiple kernel extreme learning machine (MKELM) model combining the ReliefF with nature-inspired methods is proposed for intrusion detection. The MKELM is designed to estimate whether the attack is carried out and the ReliefF is used as a preprocessor of MKELM to select appropriate features. In addition, the nature-inspired methods whose fitness functions are defined based on the kernel alignment are employed to build the optimal composite kernel in the MKELM. The KDD99, NSL and Kyoto datasets are used to evaluate the performance of the model. The experimental results indicate that the optimal composite kernel function can be determined by using any heuristic optimization method, including PSO, GA, GWO, BA and DE. Since the filter-based feature selection method is combined with the multiple kernel learning approach independent of the classifier, the proposed model can have a good performance while saving a lot of training time.

• 한국통신학회논문지
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• 제32권9C호
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• pp.861-866
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• 2007

본 논문은 가우시안 확률분포함수 (Gaussian Probability Distribution Function) 데이터 군집화를 위해 중심신경망 (Centroid Neural Network, CNN)에 Bhattacharyya 커널을 적용한 군집화 알고리즘 (Bhattacharyya Kernel based CNN, BK-CNN)을 제안한다. 제안된 BK-CNN은 무감독 알고리즘인 중심신경망을 기반으로 하고 있으며, 커널 방법을 이용하여 데이터를 특징공간에서 투영한다. 입력공간의 비선형 문제를 선형적으로 해결하기 위해 제안한 커널 방법인데, 확률분포 사이의 거리측정을 위해 Bhattacharyya 거리를 이용한 커널방법을 사용하였다. 제안된 BK-CNN을 영상데이터 분류의 문제에 적용했을 때, 제안된 BK-CNN 알고리즘이 Bhattacharyya 커널을 적용한 k-means, 자기조직지도(Self-Organizing Map)와 중심 신경망등의 기존 알고리즘보다 1.7% - 4.3%의 평균 분류정확도 향상을 가져옴을 확인할 수 있었다.