• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.493-499
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• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

• Journal of the Korean Chemical Society
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• v.23 no.2
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• pp.104-110
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• 1979

A new least square method for analysis of the whole time course of enzyme-catalyzed reactions is presented. This method requires only a programmable calculator with small capacity and is applicable to both uninhibited reactions and reactions inhibited by products or added compounds. This method fits the data to the nonlinear plot of substrate concentration vs. time, and, consequently, estimates the kinetic parameters better than the least square method based on linearly transformed equations.

• 한국공간정보시스템학회:학술대회논문집
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• 2005.11a
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• pp.35-39
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• 2005

선형혼합분광분석(LSU, Linear Spectral Unmixing) 모델은 위성 영상의 한 화소 값이 공간 내에 포함된 다양한 지표 대상물의 반사에너지가 혼합된 결과로 나타난다는 가정을 통해 화소이하(Sub-Pixel) 단위의 영상 분석을 수행하는 알고리즘의 한 형태이다. 분석의 결과는 한 화소에 존재하는 순수 대상물(Endmember)의 비율로 나타나며, 최소제곱법을 이용하여 결과를 도출하는 것이 일반적인 방법으로 알려져 있다. 하지만, 최소제곱법을 이용한 선형혼합분광분석모델은 기본적인 가정을 만족시키지 못하며, Endmember를 사용자가 임의로 지정해야 하기 때문에 영상 분석에 많은 어려움이 있다. 이런 단점을 극복하기 위해 무감독으로 추출된 Endmember를 이용한 제약선형분광혼합분석(Constrained Linear Spectral Unmixing) 모델을 본 연구를 통해 제안하고자 한다. 결과를 통해, 무감독 제약선형분광혼합분석 모델은 선형분광혼합분석 모델에 비해 각각의 Endmember에 대하여 제약조건을 만족하는 점유비율(Abundance) 정보를 제공하였으나, 비슷한 Endmember를 중복 추출할 수 있는 가능성도 지니고 있음을 확인할 수 있었다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.321-327
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• 2007

This study presents a new gridless finite difference method for solving elastic crack problems. The method constructs the Taylor expansion based on the MLS(Moving Least Squares) method and effectively calculates the approximation and its derivatives without differentiation process. Since no connectivity between nodes is required, the modeling of discontinuity embedded in the domain is very convenient and discontinuity effect due to crack is naturally implemented in the construction of difference equations. Direct discretization of the governing partial differential equations makes solution process faster than other numerical schemes using numerical integration. Numerical results for mode I and II crack problems demonstrates that the proposed method accurately and efficiently evaluates the stress intensity factors.

• 대한방사선방어학회:학술대회논문집
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• 2011.11a
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• pp.324-325
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• 2011

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.461-470
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• 2010

Semi supervised classification which is a method using labeled and unlabeled data has considerable attention in recent years. Among various methods the graph based manifold regularization is proved to be an attractive method. Least squares support vector machine is gaining a lot of popularities in analyzing nonlinear data. We propose a semi supervised classification algorithm using the least squares support vector machines. The proposed algorithm is based on the manifold regularization. In this paper we show that the proposed method can use unlabeled data efficiently.

• Journal of the Korea Computer Graphics Society
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• v.30 no.2
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• pp.1-9
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• 2024

In this paper, we propose a new method to visualize different vector field patterns from density data. We use moving least squares (MLS), which is used in physics-based simulations and geometric processing. However, typical MLS does not take into account the nature of density, as it is interpolated to a higher order through vector-based constraints. In this paper, we design an algorithm that incorporates Monte Carlo-based weights into the MLS to efficiently account for the density characteristics implicit in the input data, allowing the algorithm to represent different forms of white noise. As a result, we experimentally demonstrate detailed vector fields that are difficult to represent using existing techniques such as naive MLS and divergence-constrained MLS.

• The Korean Journal of Applied Statistics
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• v.34 no.2
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• pp.239-254
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• 2021

This paper studies time series analysis with estimation and forecasting for Korean COVID-19 confirmed cases, based on the approach of a heterogeneous autoregressive (HAR) model with two-piece t (TP-T) distributed errors. We consider HAR-TP-T time series models and suggest a step-by-step method to estimate HAR coefficients as well as TP-T distribution parameters. In our proposed step-by-step estimation, the ordinary least squares method is utilized to estimate the HAR coefficients while the maximum likelihood estimation (MLE) method is adopted to estimate the TP-T error parameters. A simulation study on the step-by-step method is conducted and it shows a good performance. For the empirical analysis on the Korean COVID-19 confirmed cases, estimates in the HAR-TP-T models of order p = 2, 3, 4 are computed along with a couple of selected lags, which include the optimal lags chosen by minimizing the mean squares errors of the models. The estimation results by our proposed method and the solely MLE are compared with some criteria rules. Our proposed step-by-step method outperforms the MLE in two aspects: mean squares error of the HAR model and mean squares difference between the TP-T residuals and their densities. Moreover, forecasting for the Korean COVID-19 confirmed cases is discussed with the optimally selected HAR-TP-T model. Mean absolute percentage error of one-step ahead out-of-sample forecasts is evaluated as 0.0953% in the proposed model. We conclude that our proposed HAR-TP-T time series model with optimally selected lags and its step-by-step estimation provide an accurate forecasting performance for the Korean COVID-19 confirmed cases.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.957-963
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• 2007

In this paper, Nonlinear Autoregressive (NAR) method based on Least Square-Support Vector Regression (LS-SVR) is introduced and tested for nonlinear sustained vowel modeling. In the database of total 43 sustained vowel of Benign Vocal Fold Lesions having aperiodic waveform, this nonlinear synthesizer near perfectly reproduced chaotic sustained vowels, and also conserved the naturalness of sound such as jitter, compared to Linear Predictive Coding does not keep these naturalness. However, the results of some phonation are quite different from the original sounds. These results are assumed that single-band model can not afford to control and decompose the high frequency components. Therefore multi-band model with wavelet filterbank is adopted for substituting single band model. As a results, multi-band model results in improved stability. Finally, nonlinear sustained vowel modeling using NAR based on LS-SVR can successfully reconstruct synthesized sounds nearly similar to original voiced sounds.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.467-482
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• 2023

In this paper, we present our new teaching and learning materials on gradient descent method, which is widely used in artificial intelligence, available for college mathematics. These materials provide a good explanation of gradient descent method at the level of college calculus, and the presented SageMath code can help students to solve minimization problems easily. And we introduce how to solve least squares problem using gradient descent method. This study can be helpful to instructors who teach various college-level mathematics subjects such as calculus, engineering mathematics, numerical analysis, and applied mathematics.