• Title/Summary/Keyword: Eigenvector Method

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A mathematical theory of the AHP(Analytic Hierarchy Process) and its application to assess research proposals (계층분석적 의사결정(AHP)을 이용한 연구과제 선정방법에 관한 연구)

  • Yang, Jeong-Mo;Lee, Sang-Gu
    • Communications of Mathematical Education
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    • v.22 no.4
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    • pp.459-469
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    • 2008
  • We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

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Estimating Optimal Potential Surface for Spatial Expansion of Built-up Area by Formulating WSM-AHP Method (WSM-AHP법의 정식화를 통한 주거지 확산 지역의 최적 잠재력 표면의 추정)

  • Kim, Dae-Sik
    • Journal of The Korean Society of Agricultural Engineers
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    • v.50 no.3
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    • pp.91-104
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    • 2008
  • This study developed the WSM (weighted scenario method)-AHP method that can optimize the weighting value for multi-criteria to make GIS grid-based potential surface. The potential surface has been used to simulate urban expansion using distributed cellular automata model and to generate land-use planning as basic data. This study formulated the WSM-AHP method in mathematically and applied to test region, Suwon city, which located on south area from Seoul. WSM-AHP method generates potential map for each pair of weighting value for all criteria, which one criterion is weighted with high weighting value and the others use low weighting value, considering that the summation for all criteria weighting values should be "1". The potential change rate to the step of weighted scenario for weighting value of criteria is standardized like AHP intensity matrix in this study. From the standard potential change rate, WSM-AHP intensity matrix is completed, and then the optimal weighting value is calculated from the maximum eigenvector of the WSM-AHP matrix, according to the new WSM-AHP method developed in this study. The applied results of new method showed that the optimal weighting value from WSM-AHP is more resonable than the general AHP specialists' evaluation for weighting value. The another new finding of this study is to suggest the deterministic approach to optimize the weighting value for the distributed CA model, which is used to find new city area and to generate rational land-use planning.

Comparative Performance Study of Various Algorithms Computing the Closest Voltage Collapse Point (최단 전압붕괴 임계점을 계산하는 알고리즘의 특성 비교)

  • Song, Chung-Gi;Nam, Hae-Kon
    • Proceedings of the KIEE Conference
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    • 1997.07c
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    • pp.1078-1082
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    • 1997
  • The distance in load parameter space to the closest voltage collapse point provides the worst case power margin and the left eigenvector identifies the most effective direction to steer the system to maximize voltage stability under contingency. This paper presents the results of the comparative performance study of the algorithms, which are applicable to a large scale power system, for computing the closest saddle node bifurcation (CSNB) point. Dobson's iterative method converges with robustness. However the slow process of updating the load increasing direction makes the algorithm less efficient. The direct method converges very quickly. But it diverges if the initial guess is not very close to CSNB. Zeng's method of estimating the approximate critical point in the pre-determined direction is attractive in the sense that it uses only using load flow equations. However, the method is found to be less efficient than Dobson's iterative method. It may be concluded from the above observation that the direct method with the initial values obtained by carrying out the iterative method twice is most efficient at this time and more efficient algorithms are needed for on-line application.

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Improved time delay estimation by adaptive eigenvector decomposition for two noisy acoustic sensors (잡음이 있는 두 음향 센서를 이용한 시간 지연 추정을 위한 향상된 적응 고유벡터 추정 기반 알고리즘)

  • Lim, Jun-Seok
    • The Journal of the Acoustical Society of Korea
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    • v.37 no.6
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    • pp.499-505
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    • 2018
  • Time delay estimation between two acoustic sensors is widely used in room acoustics and sonar for target position estimation, tracking and synchronization. A cross-correlation based method is representative for the time delay estimation. However, this method does not have enough consideration for the noise added to the receiving acoustic sensors. This paper proposes a new time delay estimation method considering the added noise on the receiver acoustic sensors. From comparing with the existing GCC (Generalized Cross Correlation) method, and adaptive eigen decomposition method, we show that the proposed method outperforms other methods for a colored signal source in the white Gaussian noise condition.

The Detection of Yellow Sand Dust Using the Infrared Hybrid Algorithm

  • Kim, Jae-Hwan;Ha, Jong-Sung;Lee, Hyun-Jin
    • Proceedings of the KSRS Conference
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    • 2005.10a
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    • pp.370-373
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    • 2005
  • We have developed Hybrid algorithm for yellow sand detection. Hybrid algorithm is composed of three methods using infrared bands. The first method used the differential absorption in brightness temperature difference between $11\mu m\;and\;12\mu m$ (BID _1), through which help distinguish the yellow sand from various meteorological clouds. The second method uses the brightness temperature difference between $3.7\mu m\;and\;11\mu m$ (BID_2). The technique would be most sensitive to dust loading during the day when the BID _2 is enhanced by reflection of $3.7\mu m$ solar radiation. The third one is a newly developed algorithm from our research, the so-called surface temperature variation method (STY). We have applied the three methods to MODIS for derivation of the yellow sand dust and in conjunction with the Principle Component Analysis (PCA), a form of eigenvector statistical analysis. PCI shows better results for yellow sand detection in comparison with the results from individual method. The comparison between PCI and MODIS aerosols optical depth (AOD) shows remarkable good correlations during daytime and relatively good correlations over the land.

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Normal Mode Approach to the Stability Analysis of Rossby-Haurwitz Wave

  • Jeong, Hanbyeol;Cheong, Hyeong Bin
    • Journal of the Korean earth science society
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    • v.38 no.3
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    • pp.173-181
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    • 2017
  • The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

Simple principal component analysis using Lasso (라소를 이용한 간편한 주성분분석)

  • Park, Cheolyong
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.3
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    • pp.533-541
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    • 2013
  • In this study, a simple principal component analysis using Lasso is proposed. This method consists of two steps. The first step is to compute principal components by the principal component analysis. The second step is to regress each principal component on the original data matrix by Lasso regression method. Each of new principal components is computed as the linear combination of original data matrix using the scaled estimated Lasso regression coefficient as the coefficients of the combination. This method leads to easily interpretable principal components with more 0 coefficients by the properties of Lasso regression models. This is because the estimator of the regression of each principal component on the original data matrix is the corresponding eigenvector. This method is applied to real and simulated data sets with the help of an R package for Lasso regression and its usefulness is demonstrated.

Face recognition rate comparison using Principal Component Analysis in Wavelet compression image (Wavelet 압축 영상에서 PCA를 이용한 얼굴 인식률 비교)

  • 박장한;남궁재찬
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.41 no.5
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    • pp.33-40
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    • 2004
  • In this paper, we constructs face database by using wavelet comparison, and compare face recognition rate by using principle component analysis (Principal Component Analysis : PCA) algorithm. General face recognition method constructs database, and do face recognition by using normalized size. Proposed method changes image of normalized size (92${\times}$112) to 1 step, 2 step, 3 steps to wavelet compression and construct database. Input image did compression by wavelet and a face recognition experiment by PCA algorithm. As well as method that is proposed through an experiment reduces existing face image's information, the processing speed improved. Also, original image of proposed method showed recognition rate about 99.05%, 1 step 99.05%, 2 step 98.93%, 3 steps 98.54%, and showed that is possible to do face recognition constructing face database of large quantity.

Density-based Topology Design Optimization of Piezoelectric Crystal Resonators (압전 수정진동자의 밀도법 기반 위상 최적설계)

  • Ha, Youn Doh;Byun, Taeuk;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.2
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    • pp.63-70
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    • 2014
  • Design sensitivity analysis and topology design optimization for a piezoelectric crystal resonator are developed. The piezoelectric crystal resonator is deformed mechanically when subjected to electric charge on the electrodes, or vice versa. The Mindlin plate theory with higher-order interpolations along thickness direction is employed for analyzing the thickness-shear vibrations of the crystal resonator. Thin electrode plates are masked on the top and bottom layers of the crystal plate in order to enforce to vibrate it or detect electric signals. Although the electrode is very thin, its weight and shape could change the performance of the resonators. Thus, the design variables are the bulk material densities corresponding to the mass of masking electrode plates. An optimization problem is formulated to find the optimal topology of electrodes, maximizing the thickness-shear contribution of strain energy at the desired motion and restricting the allowable volume and area of masking plates. The necessary design gradients for the thickness-shear frequency(eigenvalue) and the corresponding mode shape(eigenvector) are computed very efficiently and accurately using the analytical design sensitivity analysis method using the eigenvector expansion concept. Through some demonstrative numerical examples, the design sensitivity analysis method is verified to be very efficient and accurate by comparing with the finite difference method. It is also observed that the optimal electrode design yields an improved mode shape and thickness-shear energy.

Multivariate Classification of Choson Coins (다변수 분석법에 의한 조선시대 동전의 분류연구)

  • Lee, Chang-Keun;Kang, Hyung-Tai;Goh, Sung-Hee
    • 보존과학연구
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    • s.8
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    • pp.1-12
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    • 1987
  • Fifty ancient Korean coins originated in Choson dynasty have been determined for 9 elements such as Sn, Fe, As, Ag, Co, Sb, Ir, Ru and Ni by instrumental neutron activation analysis and for 3 elements such as Cu, Pb, and Zn by atomicalsorption spectrometry. Bronze coins originated in early days of the dynasty contain as major constituents Cu, Pb and Sn approximately in the ratio 90 : 4 : 3, where as, those in latter days contain in the ratio 7 : 2 : 0. Brass coins which had begun in 17century contain as major constituents Cu, Zn and Pb approximately in the ratio 7 : 1: 1. The multivariate date have been analyzed for the relation among elemental contents through the variance-covariance matrix. The data have been fur theranalyzed by a principal component mapping method. As the results training set of 8class have been chosen, based on the spread of sample points in an eigenvector plotand archaeolgical data such as age and the office of minting.

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