• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.05a
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• pp.245-248
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• 2003

In this paper, we propose a learning method of the performance improvement of the LVQ network using the radios of the hypersphere with the n-dimensional input vectors. The proposed method determines the reference vectors using the radius of the hypersphere include n+1 set of input vectors in the same class. In order to verify the effectiveness of the proposed method, we performed experiments on the Fisher's IRIS data. The experimental results showed that the proposed method improves considerably on the performance of the conventional LVQ network.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.267-271
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• 2005

We study hypersurfaces in the Euclidean space with the following property: the tangential part of the position vector has constant length. As a result, we prove that among the connected and complete hypersurfaces in the Euclidean space, only the hypersphere centered at the origin satisfies the property.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.42 no.4 s.304
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• pp.19-24
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• 2005

In this paper, some algorithms for robust stabilization of linerar time - invariant single - input - multi output(SIMO) systems subject to parameter perturbatations are presented. .The range of structure perturbation was obtained by using the gradient optimization algorithm. These algorithms iteratively enlarge the stability hypersphere in plant parameter space and can be used to design a robust controller to stabilize a plant subject to givien range of parameter ecxursions.

• Journal of the Korean Society of Industry Convergence
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• v.7 no.2
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• pp.215-220
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• 2004

In this paper, some algorithms for robust stabilization of linerar time - invariant single - input - multi output (SIMO) systems subject to parameter perturbatations are presented. At first, the determination algorithm of the largest stable hypersphere in the parameter space of a given characteristic polynomial with its coefficient perturbations near some stable nominal values is presented. These algorithms iteratively enlarge the stability hypersph ere in plant parameter space and can be used to design a controller to stabilize a plant subject to givien range of parameter ecxursions.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.32 no.4
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• pp.647-660
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• 2022

Recent works demonstrate that the semi-supervised anomaly detection method functions quite well in the environment with normal data and some anomalous data. However, abnormal data shortages can occur in an environment where it is difficult to reserve anomalous data, such as an unknown attack in the cyber security fields. In this paper, we propose ADA-PH(Abnormal Data Augmentation Method using Perturbation based on Hypersphere), a novel anomalous data augmentation method that is applicable in an environment where abnormal data is insufficient to secure the performance of the semi-supervised anomaly detection method. ADA-PH generates abnormal data by perturbing samples located relatively far from the center of the hypersphere. With the network intrusion detection datasets where abnormal data is rare, ADA-PH shows 23.63% higher AUC performance than anomaly detection without data augmentation and even performs better than the other augmentation methods. Also, we further conduct quantitative and qualitative analysis on whether generated abnormal data is anomalous.

• Kyungpook Mathematical Journal
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• v.13 no.1
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• pp.109-119
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• 1973

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.885-902
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• 2016

In this paper we begin the study of $L_k$-2-type hypersurfaces of a hypersphere ${\mathbb{S}}^{n+1}{\subset}{\mathbb{R}}^{n+2}$ for $k{\geq}1$ Let ${\psi}:M^3{\rightarrow}{\mathbb{S}}^4$ be an orientable $H_k$-hypersurface, which is not an open portion of a hypersphere. Then $M^3$ is of $L_k$-2-type if and only if $M^3$ is a Clifford tori ${\mathbb{S}}^1(r_1){\times}{\mathbb{S}}^2(r_2)$, $r^2_1+r^2_2=1$, for appropriate radii, or a tube $T^r(V^2)$ of appropriate constant radius r around the Veronese embedding of the real projective plane ${\mathbb{R}}P^2({\sqrt{3}})$.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.285-287
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• 1992

This paper considers the design of robust stabilizing controller of a linear time-invariant digital system subject to variations of parameter vector. For a given controller the radius of the largest stability hypersphere in this parameter space is calculated. This radius is a measure of the stability Margin of the closed-loop system. Based on this calculation a design procedure is proposed to robustify a given stabilizing controller. This algorithm iteratively enlarges the stability hypersphere in parameter space and can be used to design a controller to stabilize a plant subject to given ranges of parameter perturbations. These results are illustrated by an example.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.290-293
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• 1996

This paper proposes a scheme of initial cluster center selection in FCM algorithm using the genetic algorithms. The FCM algorithm often fails in the search for global optimum because it is local search techniques that search for the optimum by using hill-climbing procedures. To solve this problem, we search for a hypersphere encircling each clusters whose parameters are estimated by the genetic algorithms. Then instead of a randomized initialization for fuzzy partition matrix in FCM algorithm, we initialize each cluster center by the center of a searched hypersphere. Our experimental results show that the proposed initializing scheme has higher probabilities of finding the global or near global optimal solutions than the traditional FCM algorithm.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.665-678
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• 1997

In this paper we prove that if the minimum of the sectional curvatures of a compact n-dimensional minimal generic submanifold M of a complex projective space is 1/n, then M is the geodesic minimal hypersphere.