• 한국지능시스템학회논문지
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• 제24권5호
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• pp.529-535
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• 2014

본 논문에서는 interval type-2 possibilistic fuzzy C-means(IT2PFCM) 클러스터링 방법에 multiple Gaussian kernels을 기반으로 한 possibilistic fuzzy C-means multiple kernels(PFCM-MK) 알고리즘을 결합하여 적응적인 하이브리드 클러스터링 방법인 multiple kernels interval type-2 possibilistic fuzzy C-means(IT2PFCM-MK) 방법을 제안 하였다. 일반적으로 possibilistic fuzzy C-means(PFCM) 알고리즘은 fuzzy C-means(FCM) 알고리즘의 단점인 노이즈 민감성 및 특이점 문제와 알고리즘 초기 클러스터의 Prototype에 따라 위치가 겹치는 문제를 해결하기 위해 제안 되었다. 하지만 이 방법 역시 퍼지화 파라미터 값에 따라 위와 같은 문제를 여전히 가지고 있기 때문에 이와 같은 문제를 보완하기 위해 interval type-2 퍼지 접근 방법을 이용 하는 interval type-2 possibilistic fuzzy C-means(IT2PFCM) 알고리즘을 제안 하였다. 또한 multiple kernels 함수를 interval type-2 possibilistic fuzzy C-means(IT2PFCM) 알고리즘에 적용하여 분류하기 복잡한 형태의 데이터와 노이즈가 있는 데이터에 대하여 보다 정확하고, 향상된 클러스터링을 수행할 수 있다.

• 대한수학회지
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• 제46권3호
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• pp.523-550
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• 2009

In the paper two-weight inequalities of various type for strong fractional maximal functions and potentials with multiple kernels defined on $\mathbb{R}^2$ are established.

• 대한수학회지
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• 제61권2호
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• pp.207-226
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• 2024

In this paper, the weighted L^p boundedness of multilinear commutators and multilinear iterated commutators generated by the multilinear singular integral operators with generalized kernels and BMO functions is established, where the weight is multiple weight. Our results are generalizations of the corresponding results for multilinear singular integral operators with standard kernels and Dini kernels under certain conditions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권4호
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• pp.1463-1480
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• 2014

It is well known that sparse code is effective for feature extraction of face recognition, especially sparse mode can be learned in the kernel space, and obtain better performance. Some recent algorithms made use of single kernel in the sparse mode, but this didn't make full use of the kernel information. The key issue is how to select the suitable kernel weights, and combine the selected kernels. In this paper, we propose a novel multiple kernel sparse representation based classification for face recognition (MKSRC), which performs sparse code and dictionary learning in the multiple kernel space. Initially, several possible kernels are combined and the sparse coefficient is computed, then the kernel weights can be obtained by the sparse coefficient. Finally convergence makes the kernel weights optimal. The experiments results show that our algorithm outperforms other state-of-the-art algorithms and demonstrate the promising performance of the proposed algorithms.

• 대한수학회지
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• 제43권3호
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• pp.635-658
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• 2006

This paper is concerned with giving some rather weak size conditions implying the $L^P$ boundedness of the multiple Marcin-kiewicz integrals for some fixed $1\;<\;p\;<\;{\infty}$, which essentially improve and extend some known results.

• Communications for Statistical Applications and Methods
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• 제29권1호
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권6호
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• pp.3055-3073
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• 2019

In this paper, a new user identification method is presented using real environmental human-computer-interaction (HCI) behavior data to improve method usability. User behavior data in this paper are collected continuously without setting experimental scenes such as text length, action number, etc. To illustrate the characteristics of real environmental HCI data, probability density distribution and performance of keyboard and mouse data are analyzed through the random sampling method and Support Vector Machine(SVM) algorithm. Based on the analysis of HCI behavior data in a real environment, the Multiple Kernel Learning (MKL) method is first used for user HCI behavior identification due to the heterogeneity of keyboard and mouse data. All possible kernel methods are compared to determine the MKL algorithm's parameters to ensure the robustness of the algorithm. Data analysis results show that keyboard data have a narrower range of probability density distribution than mouse data. Keyboard data have better performance with a 1-min time window, while that of mouse data is achieved with a 10-min time window. Finally, experiments using the MKL algorithm with three global polynomial kernels and ten local Gaussian kernels achieve a user identification accuracy of 83.03% in a real environmental HCI dataset, which demonstrates that the proposed method achieves an encouraging performance.

• 호남수학학술지
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• 제32권3호
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• pp.389-397
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• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.347-354
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• 2010

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

• 대한수학회논문집
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• 제27권2호
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.