• The Korean Journal of Applied Statistics
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• v.28 no.1
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• pp.9-21
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• 2015

The support vector machine has been successfully applied to various classification areas due to its flexibility and a high level of classification accuracy. However, when analyzing imbalanced data with uneven class sizes, the classification accuracy of SVM may drop significantly in predicting minority class because the SVM classifiers are undesirably biased toward the majority class. The weighted $L_2$-norm SVM was developed for the analysis of imbalanced data; however, it cannot identify irrelevant input variables due to the characteristics of the ridge penalty. Therefore, we propose the weighted $L_1$-norm SVM, which uses lasso penalty to select important input variables and weights to differentiate the misclassification of data points between classes. We demonstrate the satisfactory performance of the proposed method through simulation studies and a real data analysis.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.109-127
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• 2007

We classify complete, locally homogeneous metrics with finite volume on four-dimensional manifolds which are critical points for the squared $L^2-norm$ functionals of either the full Riemannian curvature tensor or the Weyl curvature tensor defined on the space of Riemannian metrics.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.385-392
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• 2003

The sum Of L - R fuzzy numbers With Unbounded Supports based on Archimedean continuous f-norm T is considered. Results are more simple than those of the case for bounded supports.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.171-184
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• 2023

In this paper, we show that a complete translating soliton Σ^m in ℝⁿ for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the L^m norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L²_f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.

• Journal of the Korean housing association
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• v.2 no.1
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• pp.13-34
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• 1991

The main purpose of this study is to examine housing norm of the middle classes, housing norm and normative housing deficits by independent variables(socio - economic variables, family characteristic variable sand housing characteristic variables).There are two major findings of this study as follows :1. In the housing norm, housing space is 99.Om2, the number of rooms is 3.0, housing structure type is apartment, the maintenance cost is 13 thousand won, and housing tenure is home ownership. And housing qualify is classified into 5 dimensions, and neighborhood environment is classified into 3 dimensions.2. This thesis is to conform Morris et aL.(1984)`s hypotheses that cultural norm is homogeneous in culturally unified society and if it appears heterogeneously, It is the subject`s reporting error of the subjects confusing cultural norm with family norm.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.124-129
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• 2007

For seismic imaging and inversion, the inverted image depends on how we define the objective function. ${\ell}^1$-norm is more robust than ${\ell}^2$-norm. However, it is difficult to apply the Newton-type algorithm directly because the partial derivative for ${\ell^1$-norm has a singularity. In our paper, to overcome the difficulties of singularities, Huber function given by hybrid ${\ell}^1/{\ell}^2$-norm is used. We tested the robustness of our new object function with several noisy data set. Numerical results show that the new objective function is more robust to band limited spiky noise than the conventional object function.

• East Asian mathematical journal
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• v.14 no.2
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• pp.421-427
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• 1998

In this paper we provide sufficient conditions which ensure the strong consistency of $L_p$-norm estimation in nonlinear regression model when the probability distribution of the errors term is symmetric about zero. The least absolute deviation and least square estimation are discussed as special cases of the proposed estimation.

• Journal of the Korean Statistical Society
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• v.27 no.2
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• pp.153-163
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• 1998

We investigate density estimation problem in the L$^{\infty}$ norm and show that the iii optimal minimax rates are achieved for smooth classes of weakly dependent stationary sequences. Our results are then applied to give uniform convergence rates for various problems including the Gibbs sampler.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.17-30
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• 1997

In this work we approximate the solution of initialboun-dary value problem using a Galerkin-finite element method for the spatial discretization and Implicit Runge-Kutta method for the spatial discretization and implicit Runge-Kutta methods for the time stepping. To deal with the nonlinear term f(x, t, u), we introduce the well-known extrapolation sheme which was used widely to prove the convergence in $L_2$-norm. We present computational results showing that the optimal order of convergence arising under $L_2$-norm will be preserved in $L_{\infty}$-norm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.6
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• pp.1522-1532
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• 1996

In this paper, we compare the performance of channel estimators with the L$_{1}$-norm and L$_{2}$-norm criteria in impulaive noise environment, and show than the L$_{1}$-norm criterion is appropriate for that situation. Also, it is shown that the performance of the conventional maximum likelihood sequence detector(MLSD) can be improved by applying the same principle to mobile channels. That is, the performance of the conventional MLSD, which is known to be optimal under the Gaussian noise assumption, degrades in the impulsive noise of radio mobile communication channels. So, we proposed the MLSD which can reduce the effect of impulsive noise effectively by applying the results of channel estimators. Finally, it is confirmed by computer simulation that the performance of MLSD is significantly affected depending on the types of branch metrics, and that, in the impulsive noise environments, the proposed one with new branch metrics performs better thatn the conventional branch metric, l y(k)-s(k) l$^{[-992]}$ .