• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.295-308
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• 2016

Depending upon the nature of the problem, different divergence measures are suitable. So it is always desirable to develop a new divergence measure. In the present work, new information divergence measure, which is exponential in nature, is introduced and characterized. Bounds of this new measure are obtained in terms of various symmetric and non- symmetric measures together with numerical verification by using two discrete distributions: Binomial and Poisson. Fuzzy information measure and Useful information measure corresponding to new exponential divergence measure are also introduced.

• 한국실내디자인학회논문집
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• 제17권5호
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• pp.23-30
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• 2008

This thesis aims to analyze the visual perceptual effects drawn by 'axial composition and divergence' and to interpret the architecture of Kahn in respect of 'axial composition and divergence'. Axial composition of the form, the location of the entrance and divergence of internal movement were checked up about 53 works by extracting parti which is basic element of spatial composition. The 3D modeling simulation was performed for the selected 10 works in order to analyze the visual perceptual effect due to divergence of the internal movement. The reaction of the observer's actions and visual perception by 'axial composition and divergence' is presented in the following steps. 1. Divergence of the entrance/a panorama of expanding planes. 2. Divergence of internal movement/The process of perception of visual rotation and central spatial form. 'Perceptive form' created by 'divergence' is the result of diverse and flexible series of processes which must be experienced in person in order to reach the space as a room with a definite domain and center.

• Journal of Computing Science and Engineering
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• 제7권2호
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• pp.99-111
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• 2013

Approximating a divergence between two probability distributions from their samples is a fundamental challenge in statistics, information theory, and machine learning. A divergence approximator can be used for various purposes, such as two-sample homogeneity testing, change-point detection, and class-balance estimation. Furthermore, an approximator of a divergence between the joint distribution and the product of marginals can be used for independence testing, which has a wide range of applications, including feature selection and extraction, clustering, object matching, independent component analysis, and causal direction estimation. In this paper, we review recent advances in divergence approximation. Our emphasis is that directly approximating the divergence without estimating probability distributions is more sensible than a naive two-step approach of first estimating probability distributions and then approximating the divergence. Furthermore, despite the overwhelming popularity of the Kullback-Leibler divergence as a divergence measure, we argue that alternatives such as the Pearson divergence, the relative Pearson divergence, and the $L^2$-distance are more useful in practice because of their computationally efficient approximability, high numerical stability, and superior robustness against outliers.

• 인터넷정보학회논문지
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• 제13권1호
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• pp.1-6
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• 2012

본 논문에서는 무선인지시스템에서 효율적으로 스펙트럼 센싱을 수행하기 위해, 확률 분포 사이의 대수 차를 측정하는 Kullback-Leiber divergence기반의 새로운 스펙트럼 센싱 기술을 제안한다. 제안된 센싱 기법은 특정 센싱 구간에서의 국부 센싱 측정값들이 잡음 분포에서 발생하였는지, 기사용자 신호에서 발생하였는지를 Kullback-Leiber divergenc를 이용하여 판단한다. 시뮬레이션 을 통해, 제안된 Kullback-Leiber divergence기반의 스펙트럼 센싱 기법이 동일 조건에서 에너지 검출 기반의 스펙트럼 센싱 기법보다 더 좋은 성능을 제공할 수 있음을 보였다. 특히, 페이딩 환경 및 기사용자 신호의 SNR값이 낮은 경우에 에너지 검출 기반의 스펙트럼센싱 기법과 비교할 때 제안된 기법의 성능이 크게 향상됨을 보였다.

• 한국세라믹학회지
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• 제47권1호
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• pp.8-18
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• 2010

When metal oxides are exposed to chemical potential gradients, ions are driven to diffusive mass transport. During this transport process, the divergence of ionic fluxes offers the formation/annihilation of oxides. Therefore, the divergence of ionic flux may play an important role in the void formation in oxides. Kinetic equations were derived for describing chemical potential distribution, ionic fluxes and their divergence in oxides. The divergence was found to be the measure of void formation. Defect chemistry in scales is directly related to the sign of divergence and gives an indication of the void formation behavior. The quantitative estimation on the void formation was successfully applied to a growing magnetite scale in high temperature oxidation of iron at 823 K.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권3호
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• pp.107-116
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• 2021

We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.349-371
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• 2018

Some inequalities for quantum f-divergence of matrices are obtained. It is shown that for normalised convex functions it is nonnegative. Some upper bounds for quantum f-divergence in terms of variational and ${\chi}^2-distance$ are provided. Applications for some classes of divergence measures such as Umegaki and Tsallis relative entropies are also given.

• 대한수학회보
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• 제51권1호
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• pp.67-76
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• 2014

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: ${\bullet}$ X is a divergence-free vector field satisfying the shadowing property. ${\bullet}$ X is a divergence-free vector field satisfying the Lipschitz shadowing property. ${\bullet}$ X is an expansive divergence-free vector field. ${\bullet}$ X has no singularities and is Anosov.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권4호
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• pp.307-315
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• 2005

There exist many measures of fuzzy directed divergence corresponding to the existing probabilistic measures. Some new measures of fuzzy divergence have been proposed which correspond to some well-known existing probabilistic measures. The essential properties of the proposed measures have been developed which contains many existing measures of fuzzy directed divergence.

• 대한수학회보
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• 제59권5호
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• pp.1167-1176
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• 2022

In this paper, we study Einstein-type manifolds generalizing static spaces and V-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then M has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.