• Communications for Statistical Applications and Methods
• /
• 제17권3호
• /
• pp.451-457
• /
• 2010

This paper considers the problem of nonparametric deconvolution density estimation when sample observa-tions are contaminated by double exponentially distributed errors. Three different deconvolution density estima-tors are introduced: a weighted kernel density estimator, a kernel density estimator based on the support vector regression method in a RKHS, and a classical kernel density estimator. The performance of these deconvolution density estimators is compared by means of a simulation study.

• 한국정보과학회:학술대회논문집
• /
• 한국정보과학회 2003년도 봄 학술발표논문집 Vol.30 No.1 (B)
• /
• pp.175-177
• /
• 2003

This paper addresses a problem of classifying human breast cancer into its subtypes. A main ingredient in our approach is kernel machines such as support vector machine (SVM). kernel principal component analysis (KPCA). and kernel partial least squares (KPLS). In the task of breast cancer classification, we employ both SVM and KPLS and compare their results. In addition to this classification. we also analyze the patterns of clinical outcomes in the feature space. In order to visualize the clinical outcomes in low-dimensional space, both KPCA and KPLS are used. It turns out that these methods are useful to identify correlations between clinical outcomes and the nonlinearly protected expression profiles in low-dimensional feature space.

• 호남수학학술지
• /
• 제35권2호
• /
• pp.235-249
• /
• 2013

It is well known that each kernel function defines primal-dual interior-point method (IPM). Most of polynomial-time interior-point algorithms for linear optimization (LO) are based on the logarithmic kernel function ([9]). In this paper we define new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has $\mathcal{O}(({\log}\;p)^{\frac{5}{2}}\sqrt{n}{\log}\;n\;{\log}\frac{n}{\epsilon})$ and $\mathcal{O}(q^{\frac{3}{2}}({\log}\;p)^3\sqrt{n}{\log}\;\frac{n}{\epsilon})$ iteration complexity for large- and small-update methods, respectively. These are currently the best known complexity results for such methods.

• 대한원격탐사학회지
• /
• 제26권6호
• /
• pp.693-703
• /
• 2010

High spectral resolution of hyperspectral data enables analysis of complex natural phenomena that is reflected on the data nonlinearly. Although many manifold learning methods have been developed for such problems, most methods do not consider the spatial correlation between samples that is inherent and useful in remote sensing data. We propose a manifold learning method which directly combines the spatial proximity and the spectral similarity through kernel PCA framework. A gain factor caused by spatial proximity is first modelled with a heat kernel, and is added to the original similarity computed from the spectral values of a pair of samples. Parameters are tuned with intelligent grid search (IGS) method for the derived manifold coordinates to achieve optimal classification accuracies. Of particular interest is its performance with small training size, because labelled samples are usually scarce due to its high acquisition cost. The proposed spatial kernel PCA (KPCA) is compared with PCA in terms of classification accuracy with the nearest-neighbourhood classification method.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제13권4호
• /
• pp.254-268
• /
• 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.

• Structural Engineering and Mechanics
• /
• 제5권2호
• /
• pp.115-126
• /
• 1997

Importance sampling methods have been developed with the aim of reducing the computational costs inherent in Monte Carlo methods. This study proposes a new algorithm called the adaptive kernel method which combines and modifies some of the concepts from adaptive sampling and the simple kernel method to evaluate the structural reliability of time variant problems. The essence of the resulting algorithm is to select an appropriate starting point from which the importance sampling density can be generated efficiently. Numerical results show that the method is unbiased and substantially increases the efficiency over other methods.

• Computers and Concrete
• /
• 제24권1호
• /
• pp.7-17
• /
• 2019

The complex phenomenon of the bond formation in geopolymer is not well understood and therefore, difficult to model. This paper present applied statistical models for evaluating the compressive strength of geopolymer. The applied statistical models studied are divided into three different categories - linear regression [least absolute shrinkage and selection operator (LASSO) and elastic net], tree regression [decision and bagging tree] and kernel methods (support vector regression (SVR), kernel ridge regression (KRR), Gaussian process regression (GPR), relevance vector machine (RVM)]. The performance of the methods is compared in terms of error indices, computational effort, convergence and residuals. Based on the present study, kernel based methods (GPR and KRR) are recommended for evaluating compressive strength of Geopolymer concrete.

• Journal of the Korean Statistical Society
• /
• 제29권3호
• /
• pp.307-313
• /
• 2000

Suppose we have a set of data X1, ···, Xn and employ kernel density estimator to estimate the marginal density of X. in this article bandwith selection problem for kernel density estimator is examined closely. In particular the Kullback-Leibler method (a bandwith selection methods based on average square error (ASE)) is considered.

• Communications for Statistical Applications and Methods
• /
• 제15권6호
• /
• pp.939-946
• /
• 2008

In this paper the support vector method is presented for the probability density function estimation when the sample observations are contaminated with random noise. The performance of the procedure is compared to kernel density estimates by the simulation study.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제9권1호
• /
• pp.111-123
• /
• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.