• Journal of the Korean Data and Information Science Society
• /
• v.23 no.2
• /
• pp.393-401
• /
• 2012

This paper deals with the estimations of the least squares support vector regression when the responses are subject to randomly right censoring. The estimation is performed via two steps - the ordinary least squares support vector regression and the least squares support vector regression with censored data. We use the empirical fact that the estimated regression functions subject to randomly right censoring are close to the true regression functions than the observed failure times subject to randomly right censoring. The hyper-parameters of model which affect the performance of the proposed procedure are selected by a generalized cross validation function. Experimental results are then presented which indicate the performance of the proposed procedure.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.5
• /
• pp.1151-1160
• /
• 2014

In DNA microarray studies, the number of genes far exceeds the number of samples and the gene expression measures are highly correlated. Partial least squares regression (PLSR) is one of the popular methods for dimensional reduction and known to be useful for the classifications of microarray data by several studies. In this study, we suggest a modified version of the partial least squares regression to analyze gene expression data with survival information. The method is designed as a new gene selection method using PLSR with an iterative procedure of imputing censored survival time. Mean square error of prediction criterion is used to determine the dimension of the model. To visualize the data, plot for variables superimposed with samples are used. The method is applied to two microarray data sets, both containing survival time. The results show that the proposed method works well for interpreting gene expression microarray data.

• Journal of Mechanical Science and Technology
• /
• v.20 no.10
• /
• pp.1567-1575
• /
• 2006

In an automatic combination weigher, the line feeders distribute the product to several weighing hoppers. The ability to supply appropriate amount of product to the weighing hoppers for each combination operation is crucial for the overall performance. Determining the right duration of operating a line feeder to supply a given amount of product becomes very challenging in case of products which are irregular in volume or specific gravity such as granular secondary processed foods. In this research, several schemes were investigated to determine the best way for a line feeder to approximate the next operating time in order to supply a set amount of irregular goods to the corresponding weighing hopper. Results obtained show that a weighted least squares method (WLS) employing 10 data points is the most effective in determining the operating times of line feeders.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.4
• /
• pp.55-68
• /
• 2007

First-order least-squares method of a distributed optimal control problem for the incompressible Navier-Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing velocity-flux variables and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $L^2$ norm of the residual equations of the system. The optimal error estimates for least-squares finite element approximations are obtained.

• Journal of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.1007-1025
• /
• 2009

First-order least-squares method of a distributed optimal control problem for the incompressible Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing the vorticity and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $H^{-1}$ and $L^2$ norms of the residual equations of the system. Finite element approximations are studied and optimal error estimates are obtained. Resulting linear system of the optimality system is symmetric and positive definite. The V-cycle multigrid method is applied to the system to test computational efficiency.

• Communications for Statistical Applications and Methods
• /
• v.28 no.1
• /
• pp.81-88
• /
• 2021

k-least quantile of squares (k-LQS) estimates are a generalization of least median of squares (LMS) estimates. They have not been used as much as LMS because their breakdown points become small as k increases. But if the size of outliers is assumed to be fixed LQS estimates yield a good fit to the majority of data and residuals calculated from LQS estimates can be a reliable tool to detect outliers. We propose to use LQS estimates for separating a clean set from the data in the context of outlyingness of the cases. Three procedures are suggested for the identification of outliers using LQS estimates. Examples are provided to illustrate the methods. A Monte Carlo study show that proposed methods are effective.

• Korean Journal of Mathematics
• /
• v.24 no.1
• /
• pp.71-79
• /
• 2016

In this paper, we determine all positive integers which cannot be represented by a sum of four squares at least 9, and prove that for each N, there are nitely many positive integers which cannot be represented by a sum of four squares at least $N^2$ except $2{\cdot}4^m$, $6{\cdot}4^m$ and $14{\cdot}4^m$ for $m{\geq}0$. As a consequence, we prove that for each $k{\geq} 5$ there are nitely many positive integers which cannot be represented by a sum of k squares at least $N^2$.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.649-656
• /
• 2005

In this paper we consider a fuzzy least absolute deviation method in order to construct fuzzy linear regression model with fuzzy input and fuzzy output. We also consider two numerical examples to evaluate an effectiveness of the fuzzy least absolute deviation method and the fuzzy least squares method.

• Communications for Statistical Applications and Methods
• /
• v.7 no.3
• /
• pp.731-739
• /
• 2000

Conditional least square estimators for the parameters of he NLAR(p) time series models are obtained. it is also shown that these estimators are consistent and asymptotically normal.

• Journal of the Korean Data and Information Science Society
• /
• v.18 no.2
• /
• pp.327-344
• /
• 2007

Ridge partial least squares regression (RPLS) is a regression method which can be obtained by combining ridge regression and partial least squares regression and is intended to provide better predictive ability and less sensitive to overfitting. In this paper, explicit expressions for the shrinkage factor of RPLS are developed. The structure of the shrinkage factor is explored and compared with those of other biased regression methods, such as ridge regression, principal component regression, ridge principal component regression, and partial least squares regression using a near infrared data set.