• Journal of the Korean Data and Information Science Society
• /
• 제15권2호
• /
• pp.449-455
• /
• 2004

Support vector machine (SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval regression models for crisp input-output data. The proposed method is based on quadratic loss SVM, which implements quadratic programming approach giving more diverse spread coefficients than a linear programming one. The proposed algorithm here is model-free method in the sense that we do not have to assume the underlying model function. Experimental result is then presented which indicate the performance of this algorithm.

• 한국데이터정보과학회:학술대회논문집
• /
• 한국데이터정보과학회 2004년도 추계학술대회
• /
• pp.53-59
• /
• 2004

Support vector machine(SVM) approach to regression can be found in information science literature. SVM implements the regularization technique which has been introduced as a way of controlling the smoothness properties of regression function. In this paper, we propose a new estimation method based on quadratic loss SVM for a linear fuzzy regression model of Tanaka's, and furthermore propose a estimation method for nonlinear fuzzy regression. This approach is a very attractive approach to evaluate nonlinear fuzzy model with crisp input and output data.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2004년도 학술발표논문집
• /
• pp.67-72
• /
• 2004

Support vector machine (SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of SVM. For data sets with crisp inputs and interval outputs, the possibility and necessity models have been recently utilized, which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one. SVM also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property In fuzzy regression. However this is not a computationally expensive way. SVM allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space. In particular, SVM is a very attractive approach to model nonlinear interval data. The proposed algorithm here is model-free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output. Experimental results are then presented which indicate the performance of this algorithm.

• 대한원격탐사학회지
• /
• 제24권3호
• /
• pp.257-266
• /
• 2008

This study presents an approach to synthesize multispectral images at a higher resolution by exploiting a high-resolution image acquired in panchromatic modality. The synthesized images should be similar to the multispectral images that would have been observed by the corresponding sensor at the same high resolution. The proposed scheme is designed to reconstruct the multispectral images at the higher resolution with as less color distortion as possible. It uses a regression model of the second order to fit panchromatic data to multispectral observations. Based on the regression model, the multispectral images at the higher spatial resolution of the panchromatic image are optimized by a quadratic programming. In this study, the new method was applied to the IKONOS 1m panchromatic and 4m multispectral data, and the results were compared with them of several current approaches. Experimental results demonstrate that the proposed scheme can achieve significant improvement over other methods.

• Journal of the Korean Data and Information Science Society
• /
• 제26권6호
• /
• pp.1537-1545
• /
• 2015

Support vector quantile regression (SVQR) can be obtained by applying support vector machine with a check function instead of an e-insensitive loss function into the quantile regression, which still requires to solve a quadratic program (QP) problem which is time and memory expensive. In this paper we propose an SVQR whose objective function is composed of an asymmetric quadratic loss function. The proposed method overcomes the weak point of the SVQR with the check function. We use the iterative procedure to solve the objective problem. Furthermore, we introduce the generalized cross validation function to select the hyper-parameters which affect the performance of SVQR. Experimental results are then presented, which illustrate the performance of proposed SVQR.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2000년도 춘계학술대회 학술발표 논문집
• /
• pp.130-133
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• 제20권3호
• /
• pp.577-585
• /
• 2009

So far in a nonparametric regression model one of the interesting problems is estimating the error variance. In this paper we propose an estimator of the mean of the squared functions which is the numerator of SNR (Signal to Noise Ratio). To estimate SNR, the mean of the squared function should be firstly estimated. Our focus is on estimating the amplitude, that is the mean of the squared functions, in a nonparametric regression using a simple linear regression model with the quadratic form of observations as the dependent variable and the function of a lag as the regressor. Our method can be extended to nonparametric regression models with multivariate functions on unequally spaced design points or clustered designed points.

• Journal of Mechanical Science and Technology
• /
• 제15권7호
• /
• pp.876-888
• /
• 2001

For a large scaled optimization based on response surface methods, an efficient quadratic approximation method is presented in the context of the trust region model management strategy. If the number of design variables is η, the proposed method requires only 2η+1 design points for one approximation, which are a center point and tow additional axial points within a systematically adjusted trust region. These design points are used to uniquely determine the main effect terms such as the linear and quadratic regression coefficients. A quasi-Newton formula then uses these linear and quadratic coefficients to progressively update the two-factor interaction effect terms as the sequential approximate optimization progresses. In order to show the numerical performance of the proposed method, a typical unconstrained optimization problem and two dynamic response optimization problems with multiple objective are solved. Finally, their optimization results compared with those of the central composite designs (CCD) or the over-determined D-optimality criterion show that the proposed method gives more efficient results than others.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1999년도 하계학술대회 논문집 G
• /
• pp.2856-2858
• /
• 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.

• Molecules and Cells
• /
• 제26권4호
• /
• pp.338-343
• /
• 2008

An embryonic stem cell is a powerful tool for investigation of early development in vitro. The study of embryonic stem cell mediated neuronal differentiation allows for improved understanding of the mechanisms involved in embryonic neuronal development. We investigated expression profile changes using time course cDNA microarray to identify clues for the signaling network of neuronal differentiation. For the short time course microarray data, pattern analysis based on the quadratic regression method is an effective approach for identification and classification of a variety of expressed genes that have biological relevance. We studied the expression patterns, at each of 5 stages, after neuronal induction at the mRNA level of embryonic stem cells using the quadratic regression method for pattern analysis. As a result, a total of 316 genes (3.1%) including 166 (1.7%) informative genes in 8 possible expression patterns were identified by pattern analysis. Among the selected genes associated with neurological system, all three genes showing linearly increasing pattern over time, and one gene showing decreasing pattern over time, were verified by RT-PCR. Therefore, an increase in gene expression over time, in a linear pattern, may be associated with embryonic development. The genes: Tcfap2c, Ttr, Wnt3a, Btg2 and Foxk1 detected by pattern analysis, and verified by RT-PCR simultaneously, may be candidate markers associated with the development of the nervous system. Our study shows that pattern analysis, using the quadratic regression method, is very useful for investigation of time course cDNA microarray data. The pattern analysis used in this study has biological significance for the study of embryonic stem cells.