• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.51-56
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• 2005

There are many sources of systematic variations in cDNA microarray experiments which affect the measured gene expression levels like differences in labeling efficiency between the two fluorescent dyes. Print-tip lowess normalization is used in situations where dye biases can depend on spot overall intensity and/or spatial location within the array. However, print-tip lowess normalization performs poorly in situation where error variability for each gene is heterogeneous over intensity ranges. We proposed the new print-tip normalization methods based on support vector machine regression(SVMR) and support vector machine quantile regression(SVMQR). SVMQR was derived by employing the basic principle of support vector machine (SVM) for the estimation of the linear and nonlinear quantile regressions. We applied our proposed methods to previous cDNA micro array data of apolipoprotein-AI-knockout (apoAI-KO) mice, diet-induced obese mice, and genistein-fed obese mice. From our statistical analysis, we found that the proposed methods perform better than the existing print-tip lowess normalization method.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1537-1545
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• 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.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1453-1463
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• 2016

The most useful financial risk measure may be VaR (Value at Risk) which estimates the maximum loss amount statistically. The VaR tends to be estimated in many industries by using transformed univariate risk including variance-covariance matrix and a specific portfolio. Hong et al. (2016) are defined the Vector at Risk based on the multivariate quantile vector. When a specific portfolio is given, one point among Vector at Risk is founded as the best VaR which is called as an alternative VaR (AVaR). In this work, AVaRs have been investigated for multivariate normal distributions with many kinds of variance-covariance matrix and various portfolio weight vectors, and compared with VaRs. It has been found that the AVaR has smaller values than VaR. Some properties of AVaR are derived and discussed with these characteristics.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.87-98
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• 2017

The multivaiate empirical distribution function (MEDF) is defined in this work. The MEDF's expectation and variance are derived and we have shown the MEDF converges to its real distribution function. Based on random samples from bivariate standard normal distribution with various correlation coefficients, we also obtain MEDFs and propose two kinds of graphical methods to visualize MEDFs on two dimensional plane. One is represented with at most n stairs with similar arguments as the step function, and the other is described with at most n curves which look like bivariate quantile vector. Even though these two descriptive methods could be expressed with three dimensional space, two dimensional representation is obtained with ease and it is enough to explain characteristics of bivariate distribution functions. Hence, it is possible to visualize trivariate empirical distribution functions with three dimensional quantile vectors. With bivariate and four variate illustrative examples, the proposed MEDFs descriptive plots are obtained and explored.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.235-246
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• 2024

In high-dimensional data analysis, sufficient dimension reduction (SDR) has been considered as an attractive tool for reducing the dimensionality of predictors while preserving regression information. The principal support vector machine (PSVM) (Li et al., 2011) offers a unified approach for both linear and nonlinear SDR. This article comprehensively explores a variety of SDR methods based on the PSVM, which we call principal machines (PM) for SDR. The PM achieves SDR by solving a sequence of convex optimizations akin to popular supervised learning methods, such as the support vector machine, logistic regression, and quantile regression, to name a few. This makes the PM straightforward to handle and extend in both theoretical and computational aspects, as we will see throughout this article.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.421-433
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• 2017

The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. Hong et al. (2016) proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

• Journal of IKEEE
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• v.5 no.1 s.8
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• pp.1-7
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• 2001

In this paper, we have investigated the CDMA(Code Division Multiple Access) Cellular System with non-linear equalizer in reverse link channel. In general, due to unknown characteristics of channel in the wireless communication, the distribution of the observables cannot be specified by a finite set of parameters; instead, we partitioned the m-dimensional sample space Into a finite number of disjointed regions by using quantiles and a vector quantizer based on training samples. The algorithm proposed is based on a piecewise approximation to regression function based on quantiles and conditional partition moments which are estimated by Robbins Monro Stochastic Approximation (RMSA) algorithm. The resulting equalizers and detectors are robust in the sense that they are insensitive to variations in noise distributions. The main idea is that the robust equalizers and robust partition detectors yield better performance in equiprobably partitioned subspace of observations than the conventional equalizer in unpartitioned observation space under any condition. And also, we apply this idea to the CDMA system and analyze the BER performance.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.3
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• pp.117-124
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• 2021

The development of IOT technology and artificial intelligence technology is promoting the smartization of manufacturing system. In this study, data extracted from acceleration sensor and current sensor were obtained through experiments in the cutting process of SKD11, which is widely used as a material for special mold steel, and the amount of tool wear and product surface roughness were measured. SVR (Support Vector Regression) is applied to predict the roughness of the product surface in real time using the obtained data. SVR, a machine learning technique, is widely used for linear and non-linear prediction using the concept of kernel. In particular, by applying GSVQR (Generalized Support Vector Quantile Regression), overestimation, underestimation, and neutral estimation of product surface roughness are performed and compared. Furthermore, surface roughness is predicted using the linear kernel and the RBF kernel. In terms of accuracy, the results of the RBF kernel are better than those of the linear kernel. Since it is difficult to predict the amount of tool wear in real time, the product surface roughness is predicted with acceleration and current data excluding the amount of tool wear. In terms of accuracy, the results of excluding the amount of tool wear were not significantly different from those including the amount of tool wear.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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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.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.71-86
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• 2005

Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process.