• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.831-839
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• 2010

Least squares support vector machine (LS-SVM) is a kernel trick gaining a lot of popularities in the regression and classification problems. We use LS-SVM to propose a iterative algorithm for a nonlinear generalized autoregressive conditional heteroscedasticity model in the mean (GARCH-M) model to estimate the mean and the conditional volatility of stock market returns. The proposed method combines a weighted LS-SVM for the mean and unweighted LS-SVM for the conditional volatility. In this paper, we show that nonlinear GARCH-M models have a higher performance than the linear GARCH model and the linear GARCH-M model via real data estimations.

• Wind and Structures
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• v.27 no.3
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• pp.199-211
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• 2018

This paper deals with wind fragility and risk analysis of high rise buildings subjected to stochastic wind load. Conventionally, such problems are dealt in full Monte Carlo Simulation framework, which requires extensive computational time. Thus, to make the procedure computationally efficient, application of metamodelling technique in fragility analysis is explored in the present study. Since, accuracy by the conventional Least Squares Method (LSM) based metamodelling is often challenged, an efficient Moving Least Squares Method based adaptive metamodelling technique is proposed for wind fragility analysis. In doing so, artificial time history of wind load is generated by three wind field models: i.e., a simple one based on alongwind component of wind speed; a more detailed one considering coherence and wind directionality effect, and a third one considering nonstationary effect of mean wind. The results show that the proposed approach is more accurate than the conventional LSM based metamodelling approach when compared to full simulation approach as reference. At the same time, the proposed approach drastically reduces computational time in comparison to the full simulation approach. The results by the three wind field models are compared. The importance of non-linear structural analysis in fragility evaluation has been also demonstrated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.141-151
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• 2010

Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.1
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• pp.67-74
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• 2023

A meshless technique using the geometric conservation least-squares method (GC-LSM) was devised to discretize the governing equation of linear elasticity. Although the finite-element method is widely used for structural analysis, a meshless method was developed because of its advantages in a moving grid system. This work is the preliminary phase for developing a fully meshless-based fluid-structure interaction solver. In this study, Cauchy's momentum equation was discretized in strong form using GC-LSM for the structural domain, and the Newmark beta method was used for time integration. The solver was validated in 1D, 2D, and 3D benchmarking problems. Static and dynamic results were obtained. The results are more accurate than those of analytic solutions.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1147-1157
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• 1996

Nonlinear ill-posed problems arise in many application including parameter estimation and inverse scattering. We introduce a least squares regularization method to solve nonlinear ill-posed problems with constraints robustly and efficiently. The regularization method uses Trust-Region approach to handle the constraints on variables. The Generalized Cross Validation is used to choose the regularization parameter in computational tests. Numerical results are given to exhibit faster convergence of the method over other methods.

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.159-168
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• 2008

Since the term structure of interest rates (TSIR) has longitudinal data, we should consider as input variables both time left to maturity and time simultaneously to get a more useful and more efficient function estimation. However, since the resulting data set becomes very large, we need to develop a fast and reliable estimation method for large data set. Furthermore, it tends to overestimate TSIR because data are correlated. To solve these problems we propose a mixture of weighted least squares support vector machines. We recognize that the estimate is well smoothed and well explains effects of the third stock market crash in USA through applying the proposed method to the US Treasury bonds data.

• 한국지구물리탐사학회:학술대회논문집
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• 2005.05a
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• pp.227-232
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• 2005

Least squares (${\ell}^2-norm$) solutions of seismic inversion tend to be very sensitive to data points with large errors. The ${\ell}^p-norm$ minimization for $1{\le}p<2$ gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) gives efficient approximate solutions of these ${\ell}^p-norm$ problems. I propose a simple way to implement the IRLS method for a hybrid ${\ell}^1/{\ell}^2$ minimization problem that behaves as ${\ell}^2$ fit for small residual and ${\ell}^1$ fit for large residuals. Synthetic and a field-data examples demonstrates the improvement of the hybrid method over least squares when there are outliers in the data.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.2
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• pp.219-224
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• 2020

Binary classification has been broadly investigated in machine learning. In addition, binary classification can be easily extended to multi class problems. To successfully utilize machine learning methods for classification tasks, preprocessing and feature extraction steps are essential. These are important steps to improve their classification performances. In this paper, we propose a new learning method based on weighted least squares. In the weighted least squares, designing weights has a significant role. Due to this necessity, we also propose a new technique to obtain weights that can achieve feature transformation. Based on this weighting technique, we also propose a method to combine the learning and feature extraction processes together to perform both processes simultaneously in one step. The proposed method shows the promising performance on five UCI machine learning data sets.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.17-26
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• 2014

This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.