• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.17-25
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• 2006

We generalize the results about eigenvalues of random walks on central hyperplane arrangements computed by Bidigare, Hanlon and Rockmore to the cases of random walks on oriented matroids.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.402-406
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• 1990

A new approach of a time-varying switching hyperplane based on the theory of variable structure system (VSS) is proposed for the control of multivariable systems. While the conventional switching surface can net achieve the robust performance against parameter variations and disturbances before the sliding mode occurs, the proposed switching hyperplane, which is obtained from the eigen-structure assignment theory powerfully used in the linear multivariable systems, ensures the sliding mode from the initial state. And new continuous control input which guarantees the sliding mode is proposed. This new control input does not arise chattering problem which arises with the conventional control input of variable structure control systems. Through numerical examples, the expellant performances of the proposed controller are verified.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.12
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• pp.985-992
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• 2001

This paper proposes a self-organizing fuzzy modeling(SOFUM)which an create a new hyperplane shaped cluster and adjust parameters of the fuzzy model in repetition. The suggested algorithm SOFUM is composed of four steps: coarse tuning. fine tuning cluster creation and optimization of learning rates. In the coarse tuning fuzzy C-regression model(FCRM) clustering and weighted recursive least squared (WRLS) algorithm are used and in the fine tuning gradient descent algorithm is used to adjust parameters of the fuzzy model precisely. In the cluster creation, a new hyperplane shaped cluster is created by applying multiple regression to input/output data with relatively large fuzzy entropy based on parameter tunings of fuzzy model. And learning rates are optimized by utilizing meiosis-genetic algorithm in the optimization of learning rates To check the effectiveness of the suggested algorithm two examples are examined and the performance of the identified fuzzy model is demonstrated via computer simulation.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.419-422
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• 1996

In this paper, we consider variable structure controller design of a active magnetic bearing(AMB). In particular, we design a switching hyperplane, considering coupling characteristic among each magnet. This method is designed by applying decentralized control method. Controller design consist of two factors that is, one is linear control part to drive state variables to zero asymptotically and the other is a nonlinear controller part to maintain within neighborhood of switching hyperplane. Finally, A control method designed here is checked by simulation, which shows good results.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.3
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• pp.59-65
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• 1992

A modified primal-dual affine scaling algorithm for linear programming is presented. This modified algorithm generates an elipsoid containing all optimal dual solutions at each iteration, then checks whether or not a dual hyperplane intersects this ellipsoid. If the dual hyperplane has no intersection with this ellipsoid, its corresponding column must be optimal nonbasic. By condensing these columns, the size of LP problem can be reduced.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1281-1289
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• 2016

Richard Stanley suggested the problem of finding combinatorial proofs of formulas for counting regions of certain hyperplane arrangements defined by hyperplanes of the form $x_i=0$, $x_i=x_j$, and $x_i=2x_j$ that were found using the finite field method. We give such proofs, using embroidered permutations and linear extensions of posets.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.211-221
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• 2024

Parallel conics have interesting area and chord properties. In this paper, we study such properties of conics and conic hypersurfaces. First of all, we characterize conics in the plane with respect to the above mentioned properties. Finally, we establish some characterizations of hypersurfaces with centrally symmetric hyperplane sections.

• IEMEK Journal of Embedded Systems and Applications
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• v.14 no.5
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• pp.277-286
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• 2019

In this paper, we propose an efficient hyperplane generation technique to classify human activity from combination of events and sequence information obtained from multiple-event sensors. By generating hyperplane efficiently, our machine learning algorithm classify with less memory and run time than the LSVM (Linear Support Vector Machine) for embedded system. Because the fact that light weight and high speed algorithm is one of the most critical issue in the IoT, the study can be applied to smart home to predict human activity and provide related services. Our approach is based on reducing numbers of hyperplanes and utilizing robust string comparing algorithm. The proposed method results in reduction of memory consumption compared to the conventional ML (Machine Learning) algorithms; 252 times to LSVM and 34,033 times to LSTM (Long Short-Term Memory), although accuracy is decreased slightly. Thus our method showed outstanding performance on accuracy per hyperplane; 240 times to LSVM and 30,520 times to LSTM. The binarized image is then divided into groups, where each groups are converted to binary number, in order to reduce the number of comparison done in runtime process. The binary numbers are then converted to string. The test data is evaluated by converting to string and measuring similarity between hyperplanes using Levenshtein algorithm, which is a robust dynamic string comparing algorithm. This technique reduces runtime and enables the proposed algorithm to become 27% faster than LSVM, and 90% faster than LSTM.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2005.11a
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• pp.158-161
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• 2005

In this study, the defect diagnosis of the gas turbine engine was tried using Support Vector Machine(SVM). It is known that SVM can find the optimal solution mathematically through classifying two groups and searching for the Hyperplane of the arbitrary nonlinear boundary. The method for the decision of the gas turbine defect quantitatively was proposed using the Multi Layer SVM for classifying two groups and it was verified that SVM was shown quicker and more reliable diagnostic results than the existing Multi Layer Perceptron(MLP).

• Proceedings of the Korean Society of Computer Information Conference
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• 2019.07a
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• pp.115-116
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• 2019

SVM (Support Vector Machine)은 견고성으로 인해 다양한 분류 문제에 적용 할 수 있는 효율적인 기계 학습 기술이다. 그러나 훈련 데이터의 수가 증가함에 따라 시간 복잡도가 급격히 증가하므로 대규모 데이터 세트의 경우 SVM이 비실용적이다. 본 논문에서는 SVM을 사용하여 중복 된 학습 데이터를 효율적으로 제거하는 새로운 병렬 평면(Parallel Hyperplane) 기법을 소개한다. 제안 기법에서 PH는 재귀 적으로 형성되는 반면 PH의 외부에 있는 데이터 포인트의 클러스터는 매 반복마다 제거된다. 시뮬레이션 결과 제안 기법은 기존의 클러스터링 기반 감축 기법과 SMO 기법에 비해 학습 시간을 크게 단축시키면서 데이터 축소 없이 분류의 정확성을 높일 수 있음을 확인 하였다.