• Journal of the Korean Data and Information Science Society
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• 제14권2호
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• pp.337-343
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• 2003

In this paper we present the prediction interval estimation method using bootstrap method for least squares support vector machine(LS-SVM) regression, which allows us to perform even nonlinear regression by constructing a linear regression function in a high dimensional feature space. The bootstrap method is applied to generate the bootstrap sample for estimation of the covariance of the regression parameters consisting of the optimal bias and Lagrange multipliers. Experimental results are then presented which indicate the performance of this algorithm.

• Journal of the Korean Data and Information Science Society
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• 제24권2호
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• pp.391-399
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• 2013

Partially linear regression is capable of providing more complete description of the linear and nonlinear relationships among random variables. In support vector regression (SVR) the hyper-parameters are known to affect the performance of regression. In this paper we propose an iterative reweighted least squares (IRWLS) procedure to solve the quadratic problem of partially linear support vector regression with a modified loss function, which enables us to use the generalized approximate cross validation function to select the hyper-parameters. Experimental results are then presented which illustrate the performance of the partially linear SVR using IRWLS procedure.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.879-886
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• 2009

본 논문에서는 시장점유율을 추정할 때 최소제곱 서포트벡터기계를 적용하여 보통최소제곱과 최소제곱 서포트벡터기계의 성능을 비교하고자 한다. 최소제곱 서포트벡터기계는 커널 함수를 사용함으로 고차원의 특징 공간에서 선형회귀로 재구성함으로 비선형 회귀문제까지도 해결할 수 있는 장점을 가지고 있다. 그래서 본 논문에서는 비모수 기법인 최소제곱 서포트벡터기계를 이용하여 시장점유율 모형을 추정하고자 한다. 최소제곱 서포트벡터기계를 기반으로 한 모형 추정은 시장점유율 유인모형을 해결하기 위한 좋은 대안이 된다. 최소제곱 서포트벡터기계의 성능을 평가하기 위해 비교 실험에서는 한국 자동차 시장에서 차량 판매량을 이용하여 브랜드별 시장점유율 모형을 추정하였다.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.873-878
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• 2003

LS-SVM(Least-Squares Support Vector Machine) has been used as a promising method for regression as well as classification. Suykens et al.(2000) used only the magnitude of residuals to obtain SVs(Support Vectors). Suykens' method behaves well for homogeneous model. But in a heteroscedastic model, the method shows a poor behavior. The present paper proposes a new method to get SVs. The proposed method uses the variance of noise as well as the magnitude of residuals to obtain support vectors. Through the simulation study we justified excellence of our proposed method.

• Communications for Statistical Applications and Methods
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• 제17권2호
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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.

• 한국지능시스템학회논문지
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• 제13권4호
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• pp.486-490
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• 2003

Software qualify models can predict the risk of faults in the software early enough for cost-effective prevention of problems. This paper introduces a least squares support vector machine (LS-SVM) as a fuzzy regression method for predicting fault ranges in the software under development. This LS-SVM deals with the fuzzy data with crisp inputs and fuzzy output. Predicting the exact number of bugs in software is often not necessary. This LS-SVM can predict the interval that the number of faults of the program at each session falls into with a certain possibility. A case study on software reliability problem is used to illustrate the usefulness of this LS -SVM.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.1087-1094
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• 2005

e-insensitive support vector regression(e-SVR) is capable of providing more complete description of the linear and nonlinear relationships among random variables. In this paper we propose an iterative reweighted least squares(IRWLS) procedure to solve the quadratic problem of e-SVR with a modified loss function. Furthermore, we introduce the generalized approximate cross validation function to select the hyperparameters which affect the performance of e-SVR. Experimental results are then presented which illustrate the performance of the IRWLS procedure for e-SVR.

• Journal of the Korean Data and Information Science Society
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• 제21권2호
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• pp.363-369
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• 2010

In this paper we propose a mixed-effects least squares support vector regression (LS-SVR) for longitudinal data. We add a random-effect term in the optimization function of LS-SVR to take random effects into LS-SVR for analyzing longitudinal data. We also present the model selection method that employs generalized cross validation function for choosing the hyper-parameters which affect the performance of the mixed-effects LS-SVR. A simulated example is provided to indicate the usefulness of mixed-effect method for analyzing longitudinal data.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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• pp.735-744
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• 2007

Support vector machine(SVM) is capable of providing a more complete description of the linear and nonlinear relationships among random variables. In this paper we propose a sparse kernel regression(SKR) to overcome a weak point of SVM, which is, the steep growth of the number of support vectors with increasing the number of training data. The iterative reweighted least squares(IRWLS) procedure is used to solve the optimal problem of SKR with a Laplacian prior. Furthermore, the generalized cross validation(GCV) function is introduced to select the hyper-parameters which affect the performance of SKR. Experimental results are then presented which illustrate the performance of the proposed procedure.

• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.931-939
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• 2014

In this paper we propose the iteratively reweighted least squares procedure to solve the quadratic programming problem of support vector expectile regression with an asymmetrically weighted squares loss function. The proposed procedure enables us to select the appropriate hyperparameters easily by using the generalized cross validation function. Through numerical studies on the artificial and the real data sets we show the effectiveness of the proposed method on the estimation performances.