• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.507-513
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• 2004

Least-squares support vector machine (LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. In this paper, we propose LS-SVM approach to evaluating fuzzy regression model with multiple crisp inputs and a Gaussian fuzzy output. The proposed algorithm here is model-free method in the sense that we do not need assume the underlying model function. Experimental result is then presented which indicate the performance of this algorithm.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1001-1016
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• 2019

We are concerned with optimization methods for the $L^2$-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present an implementable (accelerated) gradient method for finding the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.643-654
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• 2021

In this paper, we define a modified q-poly-Bernoulli polynomials of the first type and modified q-poly-tangent polynomials of the first type by using q-polylogarithm function. We derive some identities of the modified polynomials with Gaussian binomial coefficients. We also explore several relations that are connected with the q-analogue of Stirling numbers of the second kind.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.1-11
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• 2024

In this paper, we define a new fully modified q-poly-Euler numbers and polynomials of the first type by using q-polylogarithm function. We derive some identities of the modified polynomials with Gaussian binomial coefficients. We also explore several relations that are connected with the q-analogue of Stirling numbers of the second kind.

• Journal of the Korea Society of Computer and Information
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• v.7 no.4
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• pp.204-210
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• 2002

The self-organizing feature map of Kohonen has disadvantage that needs too much input patterns in order to converge into the equilibrium state when it trains. In this paper we proposed the method of improving the convergence speed and rate of self-organizing feature map converting the interaction set into Dynamic Gaussian function. The proposed method Provides us with dynamic Properties that the deviation and width of Gaussian function used as an interaction function are narrowed in proportion to learning times and learning rates that varies according to topological position from the winner neuron. In this Paper. we proposed the method of improving the convergence rate and the degree of self-organizing feature map.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.12
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• pp.2418-2425
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• 1994

Although the error backpropagation(EBP) algorithm based on the gradient descent method is a widely-used learning algorithm of neural networks, learning sometimes takes a long time to acquire accuracy. This paper develops a novel learning method to alleviate the problems of EBP algorithm such as local minima, slow speed, and size of structure and thus to improve performance by adopting other new networks. Gaussian Potential Function networks(GPFN), in parallel with multilayer neural networks. Empirical simulations show the efficacy of the proposed algorithm in function approximation, which enables us to train networks faster with the better generalization capabilities.

• Proceedings of the KOSOMBE Conference
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• v.1990 no.11
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• pp.38-41
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• 1990

A new spline function for resampling discrete signal adaptively is proposed. In general, B-spline function is used for an image interpolation because of its smoothness and continuity, but accompanies a large amount of blurring effect. Hence, we developed a new spline function to remedy this effect, with two procedures ; deblurring of Gaussian blurring and diminishing of aliasing effect caused by deblurring procedure. The proposed function has a parametric expression with $\alpha$ which is related to the variance of Gaussian blurring model. Locally adaptive resampling scheme is obtained by changing a according to statistical characteristics of an image. The proposed, interpolation function shows edge-sharpening effect as well as noise smoothing, with comparison to the conventional schemes.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.885-898
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• 2012

In this paper, we consider Bayesian approaches to partially linear models, in which a regression function is represented by a semiparametric additive form of a parametric linear regression function and a nonparametric regression function. We make a comparative study on the performance of widely used Bayesian partially linear models in terms of empirical analysis. Specifically, we deal with three Bayesian methods to estimate the nonparametric regression function, one method using Fourier series representation, the other method based on Gaussian process regression approach, and the third method based on the smoothness of the function and differencing. We compare the numerical performance of three methods by the root mean squared error(RMSE). For empirical analysis, we consider synthetic data with simulation studies and real data application by fitting each of them with three Bayesian methods and comparing the RMSEs.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.1
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• pp.48.1-48.1
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• 2021

Gaussian process regression (GPR) is a powerful method used for model-independent analysis of cosmological observations. In GPR, it is important to decide an input mean function and hyperparameters that affect the reconstruction results. Depending on how the input mean function and hyperparameters are determined in the literature, I divide into four main applications for GPR and compare their results. In particular, a zero mean function is commonly used as an input mean function, which may be inappropriate for reconstructing cosmological observations such as the distance modulus. Using mock data based on Pantheon compilation of type Ia supernovae, I will point out the problem of using a zero input and suggest a new way to deal with the input mean function.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.71-84
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• 2014

By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of t, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of t, of fractional Brownian motion with Hurst parameter H = 1/4.