• Journal of the Korean Operations Research and Management Science Society
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• v.3 no.1
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• pp.75-79
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• 1978

The use of three mathematical programming techniques (quadratic programming, integer quadratic programming and linear programming) is discussed to solve some problems in linear regression analysis. When the criterion is the minimization of the sum of squared deviations and the parameters are linearly constrained, the problem may be formulated as quadratic programming problem. For the selection of variables to find "best" regression equation in statistics, the technique of integer quadratic programming is proposed and found to be a very useful tool. When the criterion of fitting a linear regression is the minimization of the sum of absolute deviations from the regression function, the problem may be reduced to a linear programming problem and can be solved reasonably well.ably well.

• 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.

• Journal of Embryo Transfer
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• v.18 no.3
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• pp.215-225
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• 2003

This study was carried out to investigate the change of blood compositions by age in Hanwoo, and a total of 866 of Hanwoo, which consisted with 638 of steer and 228 of bulls, were used to measure serum concentrations. A multiple regression equation was estimated with collection age and blood composition as independent and dependent variables, respectively. Complicated regression equations for blood compositions in steer and bulls were IGF-I(cubic), calcium (linear), and IP(linear). Linear and cubic equations were fitted to testosterone in steer and creatinine in bulls, respectively. A cubic equation in steer and linear equation in bulls were fitted to HDLC. Equations of quadratic in steer and cubic in bulls were fitted to concentration of triglyceride, globulin, and A/G ratio. BUN was fitted by equations of cubic in steer and quadratic in bulls. TP and albumin were fitted by equations of quadratic in steer and linear in bulls. A cubic regression equation did not explain the change of cortisol by age in steer and bulls. A cubic regression equation did explain the change of glucose by age in steer, but not in bulls. Higher R-square values (R-SQUARE>0.1) were estimated to IGF-1, albumin, creatinine, Inorganic phosphorous(IP) and HDLC in steer, and testosterone, IGF-I, TP, albumin, glucose, creatinine, IP, and HDLC in bulls for the fitted regression equations of blood compositions. Therefore, IGF-I, albumin, creatinine, IP, and HDLC were regarded as comparatively large variation by age in steer and bulls.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.130-133
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• 2000

In this paper, a new design methodology named FNNN(Fuzzy Polynomial Neural Network) algorithm is proposed to identify the structure and parameters of fuzzy model using PNN(Polynomial Neural Network) structure and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and modified quadratic besides the biquadratic polynomial used in the GMDH. The premise of fuzzy inference rules defines by triangular and gaussian type membership function. The fuzzy inference method uses simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture Several numerical example are used to evaluate the performance of out proposed model. Also we used the training data and testing data set to obtain a balance between the approximation and generalization of proposed model.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.12 no.4
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• pp.354-362
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• 2000

Optimal supervisory control strategy for the set points of controlled variables in the central cooling system has been studied by computer simulation. A quadratic linear regression equation for predicting the total cooling system power in terms of the controlled and uncontrolled variables was developed using simulated data collected under different values of controlled and uncontrolled variables. The optimal set temperatures such as supply air temperature, chilled water temperature, and condenser water temperature, are determined such that energy consumption is minimized as uncontrolled variables, load, ambient wet bulb temperature, and sensible heat ratio, are changed. The chilled water loop pump and cooling tower fan speeds are controlled by the PID controller such that the supply air and condenser water set temperatures reach the set points designated by the optimal supervisory controller. The influences of the controlled variables on the total system and component power consumption was determined. It is possible to minimize total energy consumption by selecting the optimal set temperatures through the trade-off among the component powers. The total system power is minimized at lower supply, higher chilled water, and lower condenser water set temperature conditions.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2856-2858
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• 1999

In this paper, the FPNN(Fuzzy Polynomial Neural Networks) algorithm with multi-layer fuzzy inference structure is proposed for the model identification of a complex nonlinear system. The FPNN structure is generated from the mutual combination of PNN (Polynomial Neural Network) structure and fuzzy inference method. The PNN extended from the GMDH(Group Method of Data Handling) uses several types of polynomials such as linear, quadratic and modifled quadratic besides the biquadratic polynomial used in the GMDH. In the fuzzy inference method, simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used Each node of the FPNN is defined as a fuzzy rule and its structure is a kind of fuzzy-neural networks. Gas furnace data used to evaluate the performance of our proposed model.

• Korean Journal of Remote Sensing
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• v.33 no.4
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• pp.401-410
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• 2017

Estimation of snow depth using optical image is conducted by using correlation with Snow Cover Fraction (SCF). Various algorithms have been proposed for the estimation of snow cover fraction based on Normalized Difference Snow Index (NDSI). In this study we tested linear, quadratic, and exponential equations for the generation of snow cover fraction maps using data from the Moderate Resolution Imaging Spectroradiometer (MODIS) Aqua satellite in order to evaluate their applicability to the complex terrain of South Korea and to search for improvements to the estimation of snow depth on this landscape. The results were validated by comparison with in-situ snowfall data from weather stations, with Root Mean Square Error (RMSE) calculated as 3.43, 2.37, and 3.99 cm for the linear, quadratic, and exponential approaches, respectively. Although quadratic results showed the best RMSE, this was due to the limitations of the data used in the study; there are few number of in-situ data recorded on the station at the time of image acquisition and even the data is mostly recorded on low snowfall. So, we conclude that linear-based algorithms are better suited for use in South Korea. However, in the case of using the linear equation, the SCF with a negative value can be calculated, so it should be corrected. Since the coefficients of the equation are not optimized for this area, further regression analysis is needed. In addition, if more variables such as Normalized Difference Vegetation Index (NDVI), land cover, etc. are considered, it could be possible that estimation of national-scale snow depth with higher accuracy.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.675-677
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• 1998

In this paper, we propose the fuzzy inference algorithm with multi-layer structure. MFIS(Multi-layer Fuzzy Inference System) uses PNN(Polynomial Neural networks) structure and the fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Hendling), and uses several types of polynomials such as linear, quadratic and cubic, as well as the biquadratic polynomial used in the GMDH. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here, the regression polynomial inference is based on consequence of fuzzy rules with the polynomial equations such as linear, quadratic and cubic equation. Each node of the MFIS is defined as fuzzy rules and its structure is a kind of neuro-fuzzy structure. We use the training and testing data set to obtain a balance between the approximation and the generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.254-259
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• 1998

A new design methology is proposed to identify the structure and parameters of fuzzy model using PNN and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and cubic besides the biquadratic polynomial used in the GMDH. The FPNN(Fuzzy Polynomial Neural Networks) algorithm uses PNN(Polynomial Neural networks) structure and a fuzzy inference method. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here a regression polynomial inference is based on consequence of fuzzy rules with a polynomial equations such as linear, quadratic and cubic equation. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture. In this paper, we will consider a model that combines the advantage of both FPNN and PNN. Also we use the training and testing data set to obtain a balance between the approximation and generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.

• Journal of the Korean Data and Information Science Society
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• v.21 no.4
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• pp.765-775
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• 2010

For the accelerated failure time (AFT) model a lot of effort has been devoted to develop effective estimation methods. AFT model assumes a linear relationship between the logarithm of event time and covariates. In this paper we propose a semiparametric support vector machine to consider situations where the functional form of the effect of one or more covariates is unknown. The proposed estimating equation can be computed by a quadratic programming and a linear equation. We study the effect of several covariates on a censored response variable with an unknown probability distribution. We also provide a generalized approximate cross-validation method for choosing the hyper-parameters which affect the performance of the proposed approach. The proposed method is evaluated through simulations using the artificial example.