• Journal of the Korean Data Analysis Society
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• 제20권6호
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• pp.2865-2872
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• 2018

데이터 마이닝 분야에서 개발된 기법에는 연관성 규칙, 군집분석, 의사결정나무, 신경망 등 여러 가지가 있는데 이들 중에서 연관성 규칙은 지지도, 신뢰도, 그리고 향상도 등 여러 가지 연관성 평가 기준을 이용하여 항목들 간에 특정한 연관성을 탐색하는 기법이다(Park, 2014). 이러한 연관성 규칙은 Agrawal et al.(1993)이 처음 제안하였으며, 그 이후로 여러 연구자들에 의해 연구가 진행되고 있으며, 최근에는 교차 엔트로피와 관련된 연구들이 발표되고 있다(Park, 2016b). 본 논문에서는 기존에 발표된 J 측도에 방향성과 순수성을 고려한 순수 대칭적 J 측도를 제안하고 예제를 활용하여 그 유용성에 대해 알아보았다. 그 결과, 동시발생빈도가 증가함에 따라 순수 대칭적 J 측도가 기존의 J 측도와 대칭적 J 측도, 순수 교차 엔트로피 측도보다 훨씬 분명하게 변하는 것을 알 수 있었으며, 불일치빈도의 크기에 따라서도 순수 대칭적 J 측도가 변화하는 폭이 더 커짐에 따라 연관성 유무를 더 분명하게 파악할 수 있었다. 따라서 순수 대칭적 J 측도는 데이터가 존재하는 어느 분야에서든지 연관성 규칙의 평가에 적용이 가능할 것으로 생각된다.

• 호남수학학술지
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• 제8권1호
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• pp.51-74
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• 1986

The thery of measure is significant in that we extend from it to the theory of integration. AS specific metric outer measures we can take Hausdorff outer measure and Lebesgue-Stieltjes outer measure connecting measure with monotone functions.([12]) The purpose of this paper is to find some properties of Lebesgue-Stieltjes measure by extending it from $R^1$ to $R^n(n{\geq}1)$ $({\S}3)$ and differentiation of the integral defined by Borel measure $({\S}4)$. If in detail, as follows. We proved that if $_n{\lambda}_{f}^{\ast}$ is Lebesgue-Stieltjes outer measure defined on a finite monotone increasing function $f:R{\rightarrow}R$ with the right continuity, then $$_n{\lambda}_{f}^{\ast}(I)=\prod_{j=1}^{n}(f(b_j)-f(a_j))$$, where $I={(x_1,...,x_n){\mid}a_j$<$x_j{\leq}b_j,\;j=1,...,n}$. (Theorem 3.6). We've reached the conclusion of an extension of Lebesgue Differentiation Theorem in the course of proving that the class of continuous function on $R^n$ with compact support is dense in $L^p(d{\mu})$ ($1{\leq$}p<$\infty$) (Proposition 2.4). That is, if f is locally $\mu$-integrable on $R^n$, then $\lim_{h\to\0}\left(\frac{1}{{\mu}(Q_x(h))}\right)\int_{Qx(h)}f\;d{\mu}=f(x)\;a.e.(\mu)$.

• 대한수학회보
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• 제37권2호
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• pp.209-215
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• 2000

Let X be a locally convex space. A series of clearcut characterizations for the boundedness of vector measure $\mu{\;}:{\;}\sum\rightarrow{\;}X$ is obtained, e.g., ${\mu}$ is bounded if and only if ${\mu}(A_j){\;}\rightarrow{\;}0$ weakly for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$ and if and only if $\{\frac{1}{j^j}{\mu}(A_j)\}^{\infty}_{j=1}$ is bounded for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$.

• 드라이브 ㆍ 컨트롤
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• 제7권1호
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• pp.38-44
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• 2010

• 충청수학회지
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• 제23권4호
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• pp.711-720
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• 2010

In this note, we will establish the integration formulae for functionals such as $F(x)=\prod_{j=1}^{n}\;x(s_j)^2$ and $G(x)=\exp\{{\lambda}{\int}_{0}^{t}\;x(s)^2dm_L(s)\}$ in the analogue of Wiener measure space and using our formulae, we will derive some formulae for series.

• 한국지능시스템학회논문지
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• 제1권2호
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• pp.4-45
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• 1991

Measures of two types of uncertainty that coexist in the Dempster-Shafer theory are overivewed. A measure of one type of uncertainty, which expresses nonspecificity of evidential claims, is well justified on both intuitive and mathermatical grounds. Proposed measures of the other types of uncertainty, which attempt to capture conflicts among evidential claims, are shown to have some deficiencies. To alleviate these deficiencies, a new measure is proposed. This measure, which is called a measure of discord, is not only satisfactory on intuitive grounds, but has alos desirable mathematical properties. A measure of total uncertainty, which is defined as the sum of nonspecificity and discord, is also discussed. The paper focuses on conceptual issues. Mathematical properties of the measure of idscord are only stated ; their proofs are given in a companion paper.

• 호남수학학술지
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• 제29권4호
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• pp.569-576
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• 2007

Let $\cal{H}$ be a separable, infinite dimensional, complex Hilbert space. We call "an operator $\cal{T}$ acting on $\cal{H}$ has a star moment sequence supported on a set K" when there exist nonzero vectors u and v in $\cal{H}$ and a positive Borel measure ${\mu}$ such that <$T^{*j}T^ku$, v> = ${^\int\limits_{K}}\;{{\bar{z}}^j}\;{{\bar{z}}^k}\;d\mu$ for all j, $k\;\geq\;0$. We obtain a characterization to find a representing star moment measure and discuss some related properties.

• 호남수학학술지
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• 제24권1호
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• pp.121-130
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• 2002

In this paper we prove a functional central limit theorem for a field $\{X_{\underline{j}}:{\underline{j}}{\in}Z_+^d\}$ of nonstationary associated random variables with $EX{\underline{j}}=0,\;E{\mid}X_{\underline{j}}{\mid}^{r+{\delta}}<{\infty}$ for some $r>2,\;{\delta}>0$and $u(n)=O(n^{-{\nu}})$ for some ${\nu}>0$, where $u(n):=sup_{{\underline{i}}{\in}Z_+^d{\underline{j}}:{\mid}{\underline{j}}-{\underline{i}}{\mid}{\geq}n}{\sum}cov(X_{\underline{i}},\;X_{\underline{j}}),\;{\mid}{\underline{x}}{\mid}=max({\mid}x_1{\mid},{\cdots},{\mid}x_d{\mid})\;for\;{\underline{x}}{\in}{\mathbb{R}}^d$. Our investigation implies and analogous result in the case associated random measure.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제4권2호
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• pp.254-258
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• 2004

In this paper, we propose a robust speech recognition system under noisy environments. Since the presence of noise severely degrades the performance of speech recognition system, it is important to design the robust speech recognition method against noise. The proposed method adopts a new distance measure technique based on stochastic probability instead of conventional method using minimum error. For evaluating the performance of the proposed method, we compared it with conventional distance measure for the 10-isolated Korean digits with car noise. Here, the proposed method showed better recognition rate than conventional distance measure for the various car noisy environments.

• 대한수학회지
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• 제59권2호
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• pp.367-377
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• 2022

Let G be a non-discrete locally compact abelian group, and 𝜇 be a transformable and translation bounded Radon measure on G. In this paper, we construct a Segal algebra S_𝜇(G) in L¹(G) such that the generalized Poisson summation formula for 𝜇 holds for all f ∈ S_𝜇(G), for all x ∈ G. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.