• Journal of Institute of Control, Robotics and Systems
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• v.17 no.8
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• pp.768-776
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• 2011

This paper considers a data fitting problem for rational function models using the LM (Levenberg-Marquardt) optimization method. Rational function models have various merits on representing a wide range of shapes and modeling complicated structures by polynomials of low degrees in both the numerator and denominator. However, rational functions are nonlinear in the parameter vector, thereby requiring nonlinear optimization methods to solve the fitting problem. In this paper, we propose a data fitting method for rational function models based on the LM algorithm which is renowned as an effective nonlinear optimization technique. Simulations show that the fitting results are robust against the measurement noises and uncertainties. The effectiveness of the proposed method is further demonstrated by the real application to a 3D depth camera calibration problem.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.12
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• pp.2265-2267
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• 2007

The purpose of this work is to compare the local fitting and global fitting approaches while applying regression model to the PTT-BP data for the prediction of exercise blood pressures. We used linear and nonlinear regression models to represent the PTT-BP relationship during exercise. PTT-BP data were acquired both under resting state and also after cycling exercise with several load conditions. PTT was calculated as the time between R-peak of ECG and the peak of differential photo-plethysmogram. For the identification of the regression models, we used local fitting which used only the resting state data and global fitting which used the whole region of data including exercise BP. The results showed that the global fitting was superior to the local fitting in terms of the coefficient of determination and the RMS (root mean square) error between the experimental and estimated BP. The nonlinear regression model which used global fitting showed slightly better performance than the linear one (no significant difference). We confirmed that the wide-range of data is required for the regression model to appropriately predict the exercise BP.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.393-401
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• 2000

Many graphical methods have been suggested for obtaining an impression of a curvature in regression problem in which some covariates enter nonlinearly. However when true model does not belong to the class of additive models, graphical methods may contain a serious bias. A method is suggested which can avoid such bias in the fitting of nonaddive models.

• Korean Journal of Radiology
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• v.22 no.7
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• pp.1194-1202
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• 2021

Objective: To investigate the age-dependent changes in regional cerebral blood flow (CBF) in healthy adults by fitting mathematical models to imaging data. Materials and Methods: In this prospective study, 90 healthy adults underwent pseudo-continuous arterial spin labeling imaging of the brain. Regional CBF values were extracted from the arterial spin labeling images of each subject. Multivariable regression with the Akaike information criterion, link test, and F test (Ramsey's regression equation specification error test) was performed for 7 models in every brain region to determine the best mathematical model for fitting the relationship between CBF and age. Results: Of all 87 brain regions, 68 brain regions were best fitted by cubic models, 9 brain regions were best fitted by quadratic models, and 10 brain regions were best fitted by linear models. In most brain regions (global gray matter and the other 65 brain regions), CBF decreased nonlinearly with aging, and the rate of CBF reduction decreased with aging, gradually approaching 0 after approximately 60. CBF in some regions of the frontal, parietal, and occipital lobes increased nonlinearly with aging before age 30, approximately, and decreased nonlinearly with aging for the rest of life. Conclusion: In adults, the age-related perfusion patterns in most brain regions were best fitted by the cubic models, and age-dependent CBF changes were nonlinear.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.3
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• pp.17-29
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• 1995

Recently, neural network models have been employed as an alternative to regression analysis for point estimation or function fitting in various field. Thus far, however, no theoretical or empirical guides seem to exist for selecting the tool which the most suitable one for a specific function-fitting problem. In this paper, we evaluate performance of three major function-fitting techniques, regression analysis and two neural network models, back-propagation and linear-Hebbian-learning neural networks. The functions to be fitted are simple linear ones of a single independent variable. The factors considered are size of noise both in dependent and independent variables, portion of outliers, and size of the data. Based on comutational results performed in this study, some guidelines are suggested to choose the best technique that can be used for a specific problem concerned.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.6
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• pp.1087-1091
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• 2007

Exact impedance modeling of the electrode/electrolyte interface is important in bio-signal sensing electrode development. Therefore, the investigation of the equivalent circuit models for the interface has been pursued for a long time by several researchers. Previous circuit models fit the experimental results in limited conditions such as frequency range, type of electrode, or electrolyte. This paper describes a new electrical circuit model and its capability of fitting the experimental results. The proposed model consists of three resistors and two constant phase elements. Electrochemical impedance spectroscopy was used to characterize the interface for Au, Pt, and stainless steel electrode in 0.9% NaCl solution. Both the proposed model and the previous model were applied to fit the measured impedance results for comparison. The proposed model fits the experimental data more accurately than other models especially at the low frequency range, and it enables us to predict the impedance at very low frequency range, including DC, using the proposed model.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.759-768
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• 2011

Tree algorithms have been widely developed for regression problems. One of the good features of a regression tree is the flexibility of fitting because it can correctly capture the nonlinearity of data well. Especially, data with sudden structural breaks such as the price of oil and exchange rates could be fitted well with a simple mixture of a few piecewise linear regression models. Now that split points are determined by chi-squared statistics related with residuals from fitting piecewise linear models and the split variable is chosen by an objective criterion, we can get a quite reasonable fitting result which goes in line with the visual interpretation of data. The piecewise linear regression by a regression tree can be used as a good fitting method, and can be applied to a dataset with much fluctuation.

• Wind and Structures
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• v.35 no.2
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• pp.93-108
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• 2022

Steel tubular towers are commonly used in UHV and long crossing transmission lines. By considering effects of the model scale, the solidity ratio and the ratio of the mean width to the mean height, wind tunnel tests under different wind speeds on twenty tubular steel tower body models and twenty-six tubular steel cross-arm models were completed. Drag coefficients and shielding factors of the experimental tower body models and cross-arm models in wind directional axis for typical skewed angles were obtained. The influence of the lift forces on the skewed wind load factors of tubular steel tower bodies was evaluated. The skewed wind load factors, the wind load distribution factors in transversal and longitudinal direction were calculated for the tubular tower body models and cross-arm models, respectively. Fitting expressions for the skewed wind load factors of tubular steel bodies and cross-arms were determined through nonlinear fitting analysis. Parameters for skewed wind loads determined by wind tunnel tests were compared with the regulations in applicable standards. Suggestions on the drag coefficients, the skewed wind load factors and the wind load distribution factors were proposed for tubular steel transmission towers.

• Journal of KIISE:Software and Applications
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• v.36 no.10
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• pp.816-824
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• 2009

In the face space, face images due to illumination and pose variations have a nonlinear distribution. Active Appearance Models (AAM) based on the linear model have limits to the nonlinear distribution of face images. In this paper, we assume that a few clusters of face images are given; we build local AAMs according to the clusters of face images, and then select a proper AAM model during the fitting phase. To solve the problem of updating fitting parameters among the models due to the model changing, we propose to build in advance relationships among the clusters in the parameter space from the training images. In addition, we suggest a gradual model changing to reduce improper model selections due to serious fitting failures. In our experiment, we apply the proposed model to Yale Face Database B and compare it with the previous method. The proposed method demonstrated successful fitting results with strongly illuminated face images of deep shadows.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.48-54
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• 1995

A direct method for fitting analysis-of-variance models to unbalanced data is presented. This method exploits sparsity and rank deficiency of the matrix and is based on Gram-Schmidt orthogonalization of a set of sparse columns of the model matrix. The computational algorithm of the sum of squares for testing estmable hyphotheses is given.