• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1135-1143
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• 2007

The singular value decomposition and the spectral decomposition are the useful methods in the area of matrix computation for multivariate techniques such as principal component analysis and multidimensional scaling. These techniques aim to find a simpler geometric structure for the data points. The singular value decomposition and the spectral decomposition are the methods being used in these techniques for this purpose. In this paper, the singular value decomposition and the spectral decomposition are compared.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.49-66
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• 1996

The singular value decomposition is one of the most useful methods in the area of matrix computation. It gives dimension reduction which is the centeral idea in many multivariate analyses. But this method is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, we derive the resistant version of singular value decomposition for principal component analysis. And we give its statistical applications to biplot which is similar to principal component analysis in aspects of the dimension reduction of an n x p data matrix. Therefore, we derive the resistant principal component analysis and biplot based on the resistant singular value decomposition. They provide graphical multivariate data analyses relatively little influenced by outlying observations.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.407-417
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• 1995

The h-plot is a graphical technique for displaying the structure of one population's variance-covariance matrix. This follows the mathematical algorithem of the principle component biplot based on the singular value decomposition. But it is known that the singular value decomposition is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, since the mathematical algorithm of the h-plot is equivalent to that of principal component biplot of Choi and Huh (1994), we derive the resistant h-plot.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.2
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• pp.301-314
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• 2015

Aiming at accurately distinguishing modeless component and natural vibration mode terms from data series of nonlinear and non-stationary processes, such as Vortex-Induced Vibration (VIV), a new empirical mode decomposition method has been developed in this paper. The key innovation related to this technique concerns the method to decompose modeless component from non-stationary process, characterized by a predetermined 'maximum intrinsic time window' and cubic spline. The introduction of conceptual modeless component eliminates the requirement of using spurious harmonics to represent nonlinear and non-stationary signals and then makes subsequent modal identification more accurate and meaningful. It neither slacks the vibration power of natural modes nor aggrandizes spurious energy of modeless component. The scale of the maximum intrinsic time window has been well designed, avoiding energy aliasing in data processing. Finally, it has been applied to analyze data series of vortex-induced vibration processes. Taking advantage of this newly introduced empirical decomposition method and mode identification technique, the vibration analysis about vortex-induced vibration becomes more meaningful.

• Geosystem Engineering
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• v.21 no.5
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• pp.251-261
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• 2018

With the urbanization in recent years, the power line interference noise in electromagnetic signal is increasing day by day, and has gradually become an unavoidable component of noises in magnetotelluric signal detection. Therefore, a kind of power line interference noise elimination method based on independent component analysis in wavelet domain for magnetotelluric signal is put forward in this paper. The method first uses wavelet decomposition to change single-channel signal into multi-channel signal, and then takes advantage of blind source separation principle of independent component analysis to eliminate power line interference noise. There is no need to choose the layer number of wavelet decomposition and the wavelet base of wavelet decomposition according to the observed signal. On the treatment effect, it is better than the previous power line interference removal method based on independent component analysis. Through the de-noising processing to actual magnetotelluric measuring data, it is shown that this method makes both the apparent resistivity curve near 50 Hz and the phase curve near 50 Hz become smoother and steadier than before processing, i.e., it effectively eliminates the power line interference noise.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.319-330
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• 2006

A signal in real world usually composes of multiple signals having different scales of frequencies. For example sun-spot data is fluctuated over 11 year and 85 year. Economic data is supposed to be compound of seasonal component, cyclic component and long-term trend. Decomposition of the signal is one of the main topics in time series analysis. However when the signal is subject to nonstationarity, traditional time series analysis such as spectral analysis is not suitable. Huang et. at(1998) proposed data-adaptive method called empirical mode decomposition (EMD) . Due to its robustness to nonstationarity, EMD has been applied to various fields. Huang et. at, however, have not considered denoising when data is contaminated by error. In this paper we propose efficient denoising method utilizing cross-validation.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.795-806
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• 2007

We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in $K\ddot{a}hler$ manifolds of dimension ${\geq}4$, and show that the F-traceless component is invariant under concircular change. In particular, we determine $K\ddot{a}hler$ manifolds with parallel F-traceless component and improve some theorems, provided in the previous paper([2]), which are concerned with the traceless component of the conformal curvature tensor and the spectrum of the Laplacian acting on $p(0{\leq}p{\leq}2)$-forms on the manifold by using the F-traceless component.

• Transactions of the Korean hydrogen and new energy society
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• v.22 no.1
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• pp.21-28
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• 2011

Fe, Ni and Co, typical active components, were dispersed on $Al_2O_3$ and $TiO_2$ for $SO_3$ decomposition. $SO_3$ decomposition was conducted at the temperature ranges from $750^{\circ}C$ to $950^{\circ}C$ using the prepared catalysts. Alumina based catalysts showed the surface areas higher than Titania based catalysts, which resulted from spinel structure formation of alumina based catalysts. Catalytic $SO_3$ decomposition reaction rates were in the order of Fe>Co${\gg}$Ni. The metal sulfate decomposition temperature were in the order of Ni>Co>Fe from TGA/DTA analysis of metal sulfate. During $SO_3$ decomposition, metal sulfate can form on the catalysts. $SO_2$ and $O_2$ can be produced from the decomposition of metal sulfate. In that point of view, the less is the metal sulfate deomposition temperature, the higher can be the $SO_3$ decomposition activity of the metal component. Therefore, it can be concluded that metal component with the low metal sulfate decomposition temperature is the pre-requisite condition of the catalysts for $SO_3$ decomposition reaction.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.55-64
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• 2023

In this paper, we propose a two-level overlapping domain decomposition preconditioner for three dimensional vector field problems posed in H(div). We introduce a new coarse component, which reduces the computational complexity, associated with the coarse vertices. Numerical experiments are also presented.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.63-70
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• 1998

The singular value decomposition is a tool which is used to find a linear structure of reduced dimension and to give interpretation of the lower dimensional structure about multivariate data. In this paper the singular value decomposition is reviewed from both algebraic and geometric point of view and, is illustrated the way which the tool is used in the multivariate techniques finding a simpler geometric structure for the data.