• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.983-986
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• 2002

Support Vector Machine (SVM) is one of the methods of pattern recognition that separate input data using hyperplane. This method has high capability of pattern recognition by using the technique, which says kernel trick, and the Radial basis function (RBF) kernel is usually used as a kernel function in kernel trick. In this paper we propose using the q-normal distribution to the kernel function, instead of conventional RBF, and compare two types of the kernel function.

• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.133-143
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• 2000

Data from weighted distributions appear, among other situations, when some of the data are missing or are damaged, a case that is important in reliability and life testing. The kernel method for hazard rate estimation is discussed for these data where the basic large sample properties are given. As a by product, the basic properties of the kernel estimate of the distribution function for data from weighted distribution are presented.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.835-844
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• 2007

This paper considers the problem of estimating the error distribution function in nonparametric regression models. Sufficient conditions are given under which the kernel estimator of the error distribution function based on nonparametric residuals satisfies the law of iterated logarithm.

• 한국정보통신설비학회:학술대회논문집
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• 2009.08a
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• pp.382-386
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• 2009

Online or sequential learning is one of the most basic and powerful method to train neuron network, and it has been widely used in disease detection, weather prediction and other realistic classification problem. At present, there are many algorithms in this area, such as MRAN, GAP-RBFN, OS-ELM, SVM and SMC-RBF. Among them, SMC-RBF has the best performance; it has less number of hidden neurons, and best efficiency. However, all the existing algorithms use signal normal distribution as kernel function, which means the output of the kernel function is same at the different direction. In this paper, we use multi-variable normal distribution as kernel function, and derive EKF learning formulas for multi-variable normal distribution kernel function. From the result of the experience, we can deduct that the proposed method has better efficiency performance, and not sensitive to the data sequence.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.5
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• pp.561-566
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• 2021

The optimum kernel size for error-distribution estimation with given error samples cannot be used in the weight adjustment of minimum Euclidean distance between error distributions (MED) algorithms. In this paper, a new adaptive kernel estimation method for convergence enhancement of MED algorithms is proposed. The proposed method uses the average rate of change in error power with respect to a small interval of the kernel width for weight adjustment of the MED learning algorithm. The proposed kernel adjustment method is applied to experiments in communication channel compensation, and performance improvement is demonstrated. Unlike the conventional method yielding a very small kernel calculated through optimum estimation of error distribution, the proposed method converges to an appropriate kernel size for weight adjustment of the MED algorithm. The experimental results confirm that the proposed kernel estimation method for MED can be considered a method that can solve the sensitivity problem from choosing an appropriate kernel size for the MED algorithm.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.3B
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• pp.277-284
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• 2011

The limitations of existing Markov chain model for reproducing extreme rainfalls are a known problem, and the problems have increased the uncertainties in establishing water resources plans. Especially, it is very difficult to secure reliability of water resources structures because the design rainfall through the existing Markov chain model are significantly underestimated. In this regard, aims of this study were to develop a new daily rainfall simulation model which is able to reproduce both mean and high order moments such as variance and skewness using a piecewise Kernel-Pareto distribution. The proposed methods were applied to summer and fall season rainfall at three stations in Han river watershed in Korea. The proposed Kernel-Pareto distribution based Markov chain model has been shown to perform well at reproducing most of statistics such as mean, standard deviation and skewness while the existing Gamma distribution based Markov chain model generally fails to reproduce high order moments. It was also confirmed that the proposed model can more effectively reproduce low order moments such as mean and median as well as underlying distribution of daily rainfall series by modeling extreme rainfall separately.

• The Mathematical Education
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• v.31 no.2
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• pp.133-140
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• 1992

The problem of estimating a smooth distribution function F at a point $\tau$ based on randomly right censored data is treated under certain smoothness conditions on F . The asymptotic performance of a certain class of kernel estimators is compared to that of the Kap lan-Meier estimator of F($\tau$). It is shown that the .elative deficiency of the Kaplan-Meier estimate. of F($\tau$) with respect to the appropriately chosen kernel type estimate. tends to infinity as the sample size n increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.6
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• pp.2527-2545
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• 2016

Measuring the similarity of given samples is a key problem of recognition, clustering, retrieval and related applications. A number of works, e.g. kernel method and metric learning, have been contributed to this problem. The challenge of similarity learning is to find a similarity robust to intra-class variance and simultaneously selective to inter-class characteristic. We observed that, the similarity measure can be improved if the data distribution and hidden semantic information are exploited in a more sophisticated way. In this paper, we propose a similarity learning approach for retrieval and recognition. The approach, termed as LDA-FEK, derives free energy kernel (FEK) from Latent Dirichlet Allocation (LDA). First, it trains LDA and constructs kernel using the parameters and variables of the trained model. Then, the unknown kernel parameters are learned by a discriminative learning approach. The main contributions of the proposed method are twofold: (1) the method is computationally efficient and scalable since the parameters in kernel are determined in a staged way; (2) the method exploits data distribution and semantic level hidden information by means of LDA. To evaluate the performance of LDA-FEK, we apply it for image retrieval over two data sets and for text categorization on four popular data sets. The results show the competitive performance of our method.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.408-413
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• 2005

A new methodology for discrete non-Gaussian probability density estimation is investigated in this paper based on a dynamic Bayesian network (DBN) and kernel functions. The estimator consists of a DBN in which the transition distribution is represented with kernel functions. The estimator parameters are determined through a recursive learning algorithm according to the maximum likelihood (ML) scheme. A discrete-type Poisson distribution is generated in a simulation experiment to evaluate the proposed method. In addition, an unknown probability density generated by nonlinear transformation of a Poisson random variable is simulated. Computer simulations numerically demonstrate that the method successfully estimates the unknown probability distribution function (PDF).