• Title, Summary, Keyword: Non-linear regression method

### Fuzzy regression using regularlization method based on Tanaka's model

• Hong Dug-Hun;Kim Kyung-Tae
• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.4
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• pp.499-505
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• 2006
• Regularlization approach to regression can be easily found in Statistics and Information Science literature. The technique of regularlization was introduced as a way of controlling the smoothness properties of regression function. In this paper, we have presented a new method to evaluate linear and non-linear fuzzy regression model based on Tanaka's model using the idea of regularlization technique. Especially this method is a very attractive approach to model non -linear fuzzy data.

### Comparison of linear and non-linear equation for the calibration of roxithromycin analysis using liquid chromatography/mass spectrometry

• Lim, Jong-Hwan;Yun, Hyo-In
• Korean Journal of Veterinary Research
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• v.50 no.1
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• pp.11-17
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• 2010
• Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.

### Non-linear PLS based on non-linear principal component analysis and neural network (비선형 주성분해석과 신경망에 기반한 비선형 PLS)

• 손정현;정신호;송상옥;윤인섭
• 제어로봇시스템학회:학술대회논문집
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• pp.394-394
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• 2000
• This Paper proposes a new nonlinear partial least square method that extends the linear PLS. Proposed nonlinear PLS uses self-organizing feature map as PLS outer relation and multilayer neural network as PLS inner regression method.

### FUZZY REGRESSION MODEL WITH MONOTONIC RESPONSE FUNCTION

• Choi, Seung Hoe;Jung, Hye-Young;Lee, Woo-Joo;Yoon, Jin Hee
• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.973-983
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• 2018
• Fuzzy linear regression model has been widely studied with many successful applications but there have been only a few studies on the fuzzy regression model with monotonic response function as a generalization of the linear response function. In this paper, we propose the fuzzy regression model with the monotonic response function and the algorithm to construct the proposed model by using ${\alpha}-level$ set of fuzzy number and the resolution identity theorem. To estimate parameters of the proposed model, the least squares (LS) method and the least absolute deviation (LAD) method have been used in this paper. In addition, to evaluate the performance of the proposed model, two performance measures of goodness of fit are introduced. The numerical examples indicate that the fuzzy regression model with the monotonic response function is preferable to the fuzzy linear regression model when the fuzzy data represent the non-linear pattern.

• Choi, Jae-Wan;Kim, Hye-Jin;Han, You-Kyung;Kim, Yong-II
• Proceedings of the KSRS Conference
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• pp.371-374
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• 2008

### Development of the Index for Estimating the Arc Status in the Short-circuiting Transfer Region of GMA Welding (GMA용접의 단락이행영역에 있어서 아크 상태 평가를 위한 모델 개발)

• 강문진;이세헌;엄기원
• Journal of Welding and Joining
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• v.17 no.4
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• pp.85-92
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• 1999
• In GMAW, the spatter is generated because of the variation of the arc state. If the arc state is quantitatively assessed, the control method to make the spatter be reduced is able to develop. This study was attempted to develop the optimal model that could estimate the arc state quantitatively. To do this, the generated spatters was captured under the limited welding conditions, and the waveforms of the arc voltage and of the welding current were collected. From the collected waveforms, the waveform factors and their standard deviations were produced, and the linear and non-linear regression models constituted using the factors and their standard deviations are proposed to estimate the arc state. the performance test to the proposed models was practiced. Obtained results are as follow. From the results of correlation analysis between the factors and the amount of the generated spatters, the standard deviations of the waveform factors have more the multiple regression coefficients than the waveform factors. Because the correlation coefficient between T and {TEX}$T_{a}${/TEX}, and s[T] and s[{TEX}$T_{a}${/TEX}] was nearly one, it was found that these factors have the same effect to the spatter generation. In the regression models to estimate the arc state, it was fond that the linear and the non linear models were also consisted of similar factors. In addition, the linear regression model was assessed the optimal model for estimating the arc state because the variance of data was narrow and multiple regression coefficient was highest among the models. But in the welding conditions which the amount of the generated spatters were small, it was found that the non linear regression model had better the estimation performance for the spatter generation than the linear.

### Inter-comparison of Prediction Skills of Multiple Linear Regression Methods Using Monthly Temperature Simulated by Multi-Regional Climate Models (다중 지역기후모델로부터 모의된 월 기온자료를 이용한 다중선형회귀모형들의 예측성능 비교)

• Seong, Min-Gyu;Kim, Chansoo;Suh, Myoung-Seok
• Atmosphere
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• v.25 no.4
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• pp.669-683
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• 2015
• In this study, we investigated the prediction skills of four multiple linear regression methods for monthly air temperature over South Korea. We used simulation results from four regional climate models (RegCM4, SNURCM, WRF, and YSURSM) driven by two boundary conditions (NCEP/DOE Reanalysis 2 and ERA-Interim). We selected 15 years (1989~2003) as the training period and the last 5 years (2004~2008) as validation period. The four regression methods used in this study are as follows: 1) Homogeneous Multiple linear Regression (HMR), 2) Homogeneous Multiple linear Regression constraining the regression coefficients to be nonnegative (HMR+), 3) non-homogeneous multiple linear regression (EMOS; Ensemble Model Output Statistics), 4) EMOS with positive coefficients (EMOS+). It is same method as the third method except for constraining the coefficients to be nonnegative. The four regression methods showed similar prediction skills for the monthly air temperature over South Korea. However, the prediction skills of regression methods which don't constrain regression coefficients to be nonnegative are clearly impacted by the existence of outliers. Among the four multiple linear regression methods, HMR+ and EMOS+ methods showed the best skill during the validation period. HMR+ and EMOS+ methods showed a very similar performance in terms of the MAE and RMSE. Therefore, we recommend the HMR+ as the best method because of ease of development and applications.

### Application of a Non-stationary Frequency Analysis Method for Estimating Probable Precipitation in Korea (전국 확률강수량 산정을 위한 비정상성 빈도해석 기법의 적용)

• Kim, Gwang-Seob;Lee, Gi-Chun
• Journal of The Korean Society of Agricultural Engineers
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• v.54 no.5
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• pp.141-153
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• 2012
• In this study, we estimated probable precipitation amounts at the target year (2020, 2030, 2040) of 55 weather stations in Korea using the 24 hour annual maximum precipitation data from 1973 through 2009 which should be useful for management of agricultural reservoirs. Not only trend tests but also non-stationary tests were performed and non-stationary frequency analysis were conducted to all of 55 sites. Gumbel distribution was chosen and probability weighted moment method was used to estimate model parameters. The behavior of the mean of extreme precipitation data, scale parameter, and location parameter were analyzed. The probable precipitation amount at the target year was estimated by a non-stationary frequency analysis using the linear regression analysis for the mean of extreme precipitation data, scale parameter, and location parameter. Overall results demonstrated that the probable precipitation amounts using the non-stationary frequency analysis were overestimated. There were large increase of the probable precipitation amounts of middle part of Korea and decrease at several sites in Southern part. The non-stationary frequency analysis using a linear model should be applicable to relatively short projection periods.

### A Study on the Weight Estimation Model of Floating Offshore Structures using the Non-linear Regression Analysis (비선형 회귀 분석을 이용한 부유식 해양 구조물의 중량 추정 모델 연구)

• Seo, Seong-Ho;Roh, Myung-Il;Shin, Hyunkyoung
• Journal of the Society of Naval Architects of Korea
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• v.51 no.6
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• pp.530-538
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• 2014
• The weight estimation of floating offshore structures such as FPSO, TLP, semi-Submersibles, Floating Offshore Wind Turbines etc. in the preliminary design, is one of important measures of both construction cost and basic performance. Through both literature investigation and internet search, the weight data of floating offshore structures such as FPSO and TLP was collected. In this study, the weight estimation model was suggested for FPSO. The weight estimation model using non-linear regression analysis was established by fixing independent variables based on this data and the multiple regression analysis was introduced into the weight estimation model. Its reliability was within 4% of error rate.

### Penalized rank regression estimator with the smoothly clipped absolute deviation function

• Park, Jong-Tae;Jung, Kang-Mo
• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.673-683
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• 2017
• The least absolute shrinkage and selection operator (LASSO) has been a popular regression estimator with simultaneous variable selection. However, LASSO does not have the oracle property and its robust version is needed in the case of heavy-tailed errors or serious outliers. We propose a robust penalized regression estimator which provide a simultaneous variable selection and estimator. It is based on the rank regression and the non-convex penalty function, the smoothly clipped absolute deviation (SCAD) function which has the oracle property. The proposed method combines the robustness of the rank regression and the oracle property of the SCAD penalty. We develop an efficient algorithm to compute the proposed estimator that includes a SCAD estimate based on the local linear approximation and the tuning parameter of the penalty function. Our estimate can be obtained by the least absolute deviation method. We used an optimal tuning parameter based on the Bayesian information criterion and the cross validation method. Numerical simulation shows that the proposed estimator is robust and effective to analyze contaminated data.