• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.69-80
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• 2015

In this paper, the probability that a given point is covered by a random convex hull generated by independent and identically-distributed random points in a plane is studied. It is shown that such probability can be expressed in terms of an integral that can be approximated numerically by function-evaluations over the grid-points in a 2-dimensional space. The new integral representation allows such probability be computed efficiently. The computational burdens under the proposed integral representation and those in the existing literature are compared. The proposed method is illustrated through numerical examples where the random points are drawn from (i) uniform distribution over a square and (ii) bivariate normal distribution over the two-dimensional Euclidean space. The applications of the proposed method in statistics are are discussed.

• East Asian mathematical journal
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• v.33 no.3
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• pp.271-289
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• 2017

It is our purpose in this paper to introduce the concept of best random proximity pair for subsets A and B of a separable Banach space E. We prove some best random approximation and best random proximity pair theorems of certain classes of random operators, which is the stochastic verse of the deterministic results of Eldred et al. [22], Eldred et al. [18] and Eldred and Veeramani [19]. Furthermore, our results generalize and extend recent results of Okeke and Abbas [42] and Okeke and Kim [43]. Moreover, we shall apply our results to study nonlinear stochastic integral equations of the Hammerstein type.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.577-581
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• 2003

Some random fixed point theorems for weakly inward multivalued random maps are obtained in Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.33-39
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• 2005

In this paper, we prove the existence of a common random fixed point of two random multivalued generalized contractions by using functional expressions.

• Journal of Information Processing Systems
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• v.8 no.3
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• pp.421-436
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• 2012

Different types of fingerprint detection algorithms that are based on extraction of minutiae points are prevalent in recent literature. In this paper, we propose a new algorithm to locate the virtual core point/centroid of an image. The Euclidean distance between the virtual core point and the minutiae points is taken as a random variable. The mean, variance, skewness, and kurtosis of the random variable are taken as the statistical parameters of the image to observe the similarities or dissimilarities among fingerprints from the same or different persons. Finally, we verified our observations with a moment parameter-based analysis of some previous works.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.663-665
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• 1998

This paper investigates a facility location problem where there are possible demand points with demand occuring probabilites and actual distances between these points and the facility site to be determined are ambiguous, Further we define the fuzzy goal with respect to the maximum value among the actual distances between demand points and the facility. We determine the site of facility maximizing the minimal satisficing degree under the chance constraint. We propose the geometric algorithm to find this optimal site.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.405-406
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• 2006

This paper proposes the new algorithm for the extraction of the corresponding points. Our algorithm is based on RANSAC(Random Sample Consensus) with EM(Expectation-Maximization). In the procedure of RANSAC, N-points are selected by the result of EM instead of the random selection. EM+SAC algorithm is applied to the correspondence for the mosaicing.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.379-386
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• 2008

In this paper, the choice of a primary resolution and wavelet basis functions are introduced under random or irregular design points of which the sample size is free of a power of two. Most wavelet methods have used the number of the points as the primary resolution. However, it turns out that a proper primary resolution is much affected by the shape of an unknown function. The proposed methods are illustrated by some simulations.

• Economic and Environmental Geology
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• v.52 no.2
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• pp.199-212
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• 2019

In the machine learning techniques, the sampling strategy of the training data affects a performance of the prediction model such as generalizing ability as well as prediction accuracy. Especially, in landslide susceptibility analysis, the data sampling procedure is the essential step for setting the training data because the number of non-landslide points is much bigger than the number of landslide points. However, the previous researches did not consider the various sampling methods for the training data. That is, the previous studies selected the training data randomly. Therefore, in this study the authors proposed several different sampling methods and assessed the effect of the sampling strategies of the training data in landslide susceptibility analysis. For that, total six different scenarios were set up based on the sampling strategies of landslide points and non-landslide points. Then Random Forest technique was trained on the basis of six different scenarios and the attribute importance for each input variable was evaluated. Subsequently, the landslide susceptibility maps were produced using the input variables and their attribute importances. In the analysis results, the AUC values of the landslide susceptibility maps, obtained from six different sampling strategies, showed high prediction rates, ranges from 70 % to 80 %. It means that the Random Forest technique shows appropriate predictive performance and the attribute importance for the input variables obtained from Random Forest can be used as the weight of landslide conditioning factors in the susceptibility analysis. In addition, the analysis results obtained using specific sampling strategies for training data show higher prediction accuracy than the analysis results using the previous random sampling method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.1
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• pp.284-291
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• 1995

This paper proposes a method for determination of optimal reference spectrum in random vibration control. The least square method is used to minimize the spectrum deviation between the specified reference spectrum and spectra at the specimen-mounted points. This method needs only the measured FRF's at the control point and specimen-mounted points in pre-vibration test. Using the proposed method as reference spectrum, it is possible to easily predict spectra at the specimen-mounted points, and also to reduce overtest resulting from dynamic characteristics of shaker and fixture. This method is shown through theoretical and experimental results to be an effective method.