• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.4
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• pp.254-268
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• 2013

For real-world clustering tasks, the input data is typically not easily separable due to the highly complex data structure or when clusters vary in size, density and shape. Kernel-based clustering has proven to be an effective approach to partition such data. In this paper, we provide an overview of several fuzzy kernel clustering algorithms. We focus on methods that optimize an fuzzy C-mean-type objective function. We highlight the advantages and disadvantages of each method. In addition to the completely unsupervised algorithms, we also provide an overview of some semi-supervised fuzzy kernel clustering algorithms. These algorithms use partial supervision information to guide the optimization process and avoid local minima. We also provide an overview of the different approaches that have been used to extend kernel clustering to handle very large data sets.

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.111-120
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• 2016

In usual, the discontinuous variance function was estimated nonparametrically using a kernel type estimator with data sets split by an estimated location of the change point. Kang et al. (2000) proposed the Gasser-$M{\ddot{u}}ller$ type kernel estimator of the discontinuous regression function using the adjusted observations of response variable by the estimated jump size of the change point in $M{\ddot{u}}ller$ (1992). The adjusted observations might be a random sample coming from a continuous regression function. In this paper, we estimate the variance function using the Nadaraya-Watson kernel type estimator using the adjusted squared residuals by the estimated location of the change point in the discontinuous variance function like Kang et al. (2000) did. The rate of convergence of integrated squared error of the proposed variance estimator is derived and numerical work demonstrates the improved performance of the method over the exist one with simulated examples.

• Journal of Distribution Research
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• v.10 no.3
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• pp.1-14
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• 2005

It is important to control performance and a Sustainable Collaboration (SC) for the successful Supply Chain Management (SCM). This research developed a control model which analyzed SCM performances based on a Balanced Scorecard (ESC) and an SC using Support Vector Machine (SVM). 108 specialists of an SCM completed the questionnaires. We analyzed experimental data set using SVM. This research compared the forecasting accuracy of an SCMSC through four types of SVM kernels: (1) linear, (2) polynomial (3) Radial Basis Function (REF), and (4) sigmoid kernel (linear > RBF > Sigmoid > Polynomial). Then, this study compares the prediction performance of SVM linear kernel with Artificial Neural Network. (ANN). The research findings show that using SVM linear kernel to forecast an SCMSC is the most outstanding. Thus SVM linear kernel provides a promising alternative to an SC control level. A company which pursues an SCM can use the information of an SC in the SVM model.

• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.361-368
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• 1993

In recent years, kernel type estimates are abundant. In this paper, we propose a bandwidth selection method for kernel regression of fixed design based on bootstrap procedure. Mathematical properties of proposed bootstrap-based bandwidth selection method are discussed. Performance of the proposed method for small sample case is compared with that of cross-validation method via a simulation study.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.895-904
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• 2000

The contact problem of two elastic bodies of arbitrary shape with a general kernel form, investigated from Hertz problem, is reduced to an integral equation of the second kind with Cauchy kernel. A numerical method is adapted to determine the unknown potential function between the two surfaces under certain conditions. Many cases are derived and discussed from the work.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.343-358
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• 2017

Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.

• East Asian mathematical journal
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• v.37 no.3
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• pp.333-354
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• 2021

A support vector machine (SVM) is a state-of-the-art machine learning model rooted in structural risk minimization. SVM is underestimated with regards to its application to real world problems because of the difficulties associated with its use. We aim at showing that the performance of SVM highly depends on which kernel function to use. To achieve these, after providing a summary of support vector machines and kernel function, we constructed experiments with various benchmark datasets to compare the performance of various kernel functions. For evaluating the performance of SVM, the F1-score and its Standard Deviation with 10-cross validation was used. Furthermore, we used taylor diagrams to reveal the difference between kernels. Finally, we provided Python codes for all our experiments to enable re-implementation of the experiments.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1607-1619
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• 2015

We investigate some generalization of a class of Hankel-Clifford transformations having Fox H-function as part of its kernel on a class of Boehmians. The generalized transform is a one-to-one and onto mapping compatible with the classical transform. The inverse Hankel-Clifford transforms are also considered in the sense of Boehmians.

• Journal of the Korean Statistical Society
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• v.27 no.1
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• pp.113-132
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• 1998

In this paper, we consider a minimum distance (M.D.) estimation based on kernels for U-statistics. We use Cramer-von Mises type distance function which measures the discrepancy between U-empirical distribution function(d.f.) and modeled d.f. of kernel. In the distance function, we allow various integrating measures, which can be finite, $\sigma$-finite or discrete. Then we derive the asymptotic normality and study the qualitative robustness of M. D. estimates.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1049-1058
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• 2012

Nonparametric methods are often used as an alternative to parametric methods to estimate density function and regression function. In this paper we consider improved methods to select the Bezier points in Bezier curve smoothing that is shown to have the same asymptotic properties as the kernel methods. We show that the proposed methods are better than the existing methods through numerical studies.