• Journal of Computing Science and Engineering
• /
• v.7 no.2
• /
• pp.99-111
• /
• 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.

• Journal of Korean Ophthalmic Optics Society
• /
• v.14 no.4
• /
• pp.53-57
• /
• 2009

Purpose: To study the relationship of N.P.C, heterophoria and near convergence and divergence by amount of the refractive error. Methods: All subjects have no ocular disease and their mean age is 22.7. All 39 subjects examined about refractive error, near point of convergence (NPC), heterophoria, near convergence and divergence. Results: Classified by low refractive state, middle refractive state, and high refractive state compared with the expected value of Morgan. NPC had been measured within low and middle refractive state eight all the 8cm. However, high refractive state measured 9.64 cm. Low and middle refractive state for the classification by near phoria. Near esophoria groups was smallest by near divergence and exophoria groups was smallest by near convergence. Conclusions: Near convergence were largest with esophoria while near divergence were largest with exophoria.

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.733-738
• /
• 2008

Using an information of dimensions of divergence points, we give full information of dimensions of the completely decomposed class of the lower(upper) distribution sets of a self-similar Cantor set. Further using a relationship between the distribution sets and the subsets generated by the lower(upper) local dimensions of a self-similar measure, we give full information of dimensions of the subsets by the local dimensions.

• Journal of Korean Ophthalmic Optics Society
• /
• v.5 no.1
• /
• pp.101-105
• /
• 2000

This study was to investigate the effect of EEG wave type on visual cortex of visual target according to position of fixation point on the Korean. Visual evoked potential system used the BIO-Pag and recorded to 586 computer. The illumination was 500 lux and the visual target was red light dot of 3 cm size. The results of the convergence and divergence as follows: The visual stimulation waves on the visual cortex have about 70% of delta wave, about 10% of beta wave, about 9% of theta wave and about 7% of alpha wave respectively. The convergence state was much more appeared the fast wave on the comparative of the divergence. Therefore, the convergence state was much more producted the beta and alpha wave on the comparative of the divergence. On the other hand, on the convergence and divergence, the histogram amplitude of EEG wave appeared almost the non-Gaussian shape. According to the phase analysis of amplitude of EEG wave almost all type was linear shape.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.232-237
• /
• 1998

This paper describes a new method for estimating time-to-collision which exhibits high tolerance to noise contained in camera images. Time to collision (TTC) is one of the most important parameters available from a camera attached to a mobile machine. TTC indirectly stands far the translation speed of the camera and is usually calculated either from successive images or optical flow by using intimate relationship between TTC and flow divergence. In most cases, however, it is not easy to get accurate optical flow, which makes it difficult to calculate TTC. In this study it is proved that if the target has a smooth surface, the average of divergence over any point-symmetric region on the image is equal to the divergence of the center of the region. It means that required divergence can be calculated by integrating optical flow vectors over a symmetric region. It is expected that in the process of the integration, accidental noise is canceled if they are independent of optical flow and the motion of the camera. Experimental results show that TTC can be estimated regardless of the surface condition. It is also shown that influence of noise is eliminated as the area of integration increases.

• Journal of Korean Ophthalmic Optics Society
• /
• v.10 no.3
• /
• pp.205-213
• /
• 2005

To evaluate the reliability of binocular vision measurements by phorometry. 90 students volunteered to participate in this study. 25 subjects were males, and 65 were females, they ranged in ages from 21 to 30 years. All subjects had normal ocular and systematic health, and all of them had at least 1.0 visual acuity with their best correction. At negative relative convergence(NRC) measurement in distance, the percentage of subjects is included in expected value(blur point/break point/recovery point) was 78%/61%/67%, divergence excess(DE) was 9%/31%/33%, and divergence insufficience(DI) was 13%/8%/9%, respectively. And positive relative convergence(PRC) measurement, includes expected value was 20%/46%/39%, convergence excess(CE) was 22%/14%/16%, and convergence insufficience(CI) was 35%/40%/45%. AC/A ratios of 42 subjects were normal. 38 were low, and the rest of them high. A low AC/A ratio is usually the result of a small vergence response in relation to accommodation. Negative relative convergence(NRC) at near, includes expected value was 26%/29%/44%, divergence excess(DE) was 61%/33%/24%, and divergence insufficience(DI) was 3%/38%/32%. And PRC at near, includes expected value was 33%/40%/31%, convergence excess(CE) was 61%/23%/42%, and convergence insufficience(CI) was 6%/37%/27%. For the near point of convergence(NPC) test, 58% of their subjects had a break of ${\leq}8cm$ with the accommodative target. In case of NRA(PRA) measurement, the expected value was 41%(33%). Accommodative insufficiency (AI) was 33%(43%), and accommodative excess(AE) was 26%(24%), respectively. AE was related to respectively low values of NRA. AI and CE are associated with high value of NRA, and the dysfunction of convergence excess combined with AE was related to a normal-high values of NRA. PRA in AI was related to a low value, wheres the dysfunction are associated with high values of PRA.

• Journal of the Korean Statistical Society
• /
• v.30 no.2
• /
• pp.247-263
• /
• 2001

This paper concerns a problem of classification based on training dta. A framework of information geometry is given to elucidate the characteristics of discriminant functions including logistic discrimination and AdaBoost. We discuss a class of loss functions from a unified viewpoint.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.1546-1551
• /
• 2004

The laser Doppler technique is well-established as a velocity measurement technique of high precision for flow velocity. Recently, the laser Doppler technique has also been used to measure acceleration of fluid particles. Acceleration is interesting from a fluid mechanics point of view, since the Navier Stokes equations, specifically the left-hand-side, are formulated in terms of fluid acceleration. Further, there are several avenues to estimating the dissipation rate using the acceleration. However such measurements place additional demands on the design of the optical system; in particular fringe non-uniformity must be held below about 0.0001 to avoid systematic errors. Relations expressing fringe divergence as a function of the optical parameters of the system have been given in the literature; however, direct use of these formulae to minimize fringe divergence lead either to very large measurement volumes or to extremely high intersection angles. This dilemma can be resolved by using an off-axis receiving arrangement, in which the measurement volume is truncated by a pinhole in front of the detection plane. In the present study an optical design study is performed for optimizing laser Doppler systems for fluid acceleration measurements. This is followed by laboratory validation using a round free jet and a stagnation flow, two flows in which either fluid acceleration has been previously measured or in which the acceleration is known analytically. A 90 degree off-axis receiving angle is used with a pinhole or a slit.

• Nuclear Engineering and Technology
• /
• v.55 no.4
• /
• pp.1350-1364
• /
• 2023

2D/1D coupling method is an important neutron transport calculation method due to its high accuracy and relatively low computation cost. However, 2D/1D coupling method may diverge especially in small axial mesh size. To analyze the convergence behavior of 2D/1D coupling method, a Fourier analysis for k-eigenvalue neutron transport problems is implemented. The analysis results present the divergence problem of 2D/1D coupling method in small axial mesh size. Several common attempts are made to solve the divergence problem, which are to increase the number of inner iterations of the 2D or 1D calculation, and two times 1D calculations per outer iteration. However, these attempts only could improve the convergence rate but cannot deal with the divergence problem of 2D/1D coupling method thoroughly. Moreover, the choice of axial solvers, such as DGFEM SN and traditional SN, and its effect on the convergence behavior are also discussed. The results show that the choice of axial solver is a key point for the convergence of 2D/1D method. The DGFEM SN based 2D/1D method could converge within a wide range of optical thickness region, which is superior to that of traditional SN method.

• Journal of the Korean Data and Information Science Society
• /
• v.17 no.2
• /
• pp.543-557
• /
• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.