• Title/Summary/Keyword: matrix methods

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On Testing Equality of Matrix Intraclass Covariance Matrices of $K$Multivariate Normal Populations

  • Kim, Hea-Jung
    • Communications for Statistical Applications and Methods
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    • v.7 no.1
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    • pp.55-64
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    • 2000
  • We propose a criterion for testing homogeneity of matrix intraclass covariance matrices of K multivariate normal populations, It is based on a variable transformation intended to propose and develop a likelihood ratio criterion that makes use of properties of eigen structures of the matrix intraclass covariance matrices. The criterion then leads to a simple test that uses an asymptotic distribution obtained from Box's (1949) theorem for the general asymptotic expansion of random variables.

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POWER SYSTEM TRANSIENT STABILITY ANALYSIS USING TRANSITION MATRIX AND VOLTAGE DERIVATIVES (천이행렬과 전압 미분을 이용한 전력계통의 과도 안정도 해석)

  • Park, Young-Moon;Kim, Gwang-Won
    • Proceedings of the KIEE Conference
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    • 1990.07a
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    • pp.135-138
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    • 1990
  • For transient stability analysis of a power system, the new method using transition matrix is introduced in this paper. At the present the, Runge-Kutta, Modified-Euler and Trapezoidal methods have been very popular in most stability programs, Modified-Euler and Trapezoidal methods are inferior in accuracy and Runge-Kutta method has problems in computation time. The proposed algorithm requires transition matrix and its integrated values with derivatives of nonlinear parts in nonlinear differential equations for stability analysis. The method presented in this paper is between Modified-Euler and Runge-Kutta methods from the view point of computation time and is superior to the other methods in accuracy.

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Comparison of Damping Matrix Estimation Methods for Model Updating (모형개선을 위한 감쇠행렬 추정법의 비교)

  • Lee, Gun-Myung;Ju, Young-Ho;Park, Mun-Soo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.20 no.10
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    • pp.923-930
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    • 2010
  • Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping, and in the second stage, damping matrices are estimated with the mass and stiffness matrices fixed. Three methods to estimate damping matrices for this purpose are proposed in this paper. The methods include one for proportional damping systems and two for non-proportional damping systems. Method 1 utilizes orthogonality of normal modes and estimates damping matrices using the modal parameters extracted from the measured responses. Method 2 estimates damping matrices from impedance matrices which are the inverse of FRF matrices. Method 3 estimates damping using the equation which relates a damping matrix to the difference between the analytical and measured FRFs. The characteristics of the three methods are investigated by applying them to simulated discrete system data and experimental cantilever beam data.

NEW ALGORITHMS FOR SOLVING ODES BY PSEUDOSPECTRAL METHOD

  • Darvishi, M.T.
    • Journal of applied mathematics & informatics
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    • v.7 no.2
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    • pp.439-451
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    • 2000
  • To compute derivatives using matrix vector multiplication method, new algorithms were introduced in [1.2]n By these algorithms, we reduced roundoff error in computing derivative using Chebyshev collocation methods (CCM). In this paper, some applications of these algorithms ar presented.

The Development of the Integrated Nursing Practicum Education Matrix based on Learning Outcomes (학습성과기반 단계적 통합간호실습교육 매트릭스 개발)

  • Lee, JuHee;Lee, Taewha;Lee, Hyunkyeong;Kim, Sanghee;Bae, Juyeon;Han, Jeehee;Lee, Kyongeun
    • The Journal of Korean Academic Society of Nursing Education
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    • v.21 no.4
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    • pp.528-539
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    • 2015
  • Purpose: The purpose of this study was to develop an integrated nursing practicum education matrix based on the learning outcomes of each stage. Methods: In this Delphi technique study, 10 experts, consisting of six professors and four nurses, participated in the development of the matrix. The first step was an in-depth review for the composition of the questionnaire and the second step was the Delphi technique. The Delphi survey was conducted two times in order to complete the components of the matrix. The survey data was analyzed for statistical averages and standard deviations to decide the order of priority. Results: According to each stage (i.e. fundamental stage, competent stage, and proficient stage), the matrix was composed of education contents, methods, evaluation methods, and curriculum outcomes. Conclusion: The integrated nursing practicum education matrix of Y University was completed. The developed matrix will result in a reduction in the gap between nursing education and clinical practice and an improvement in nursing competency.

Magnifying Block Diagonal Structure for Spectral Clustering (스펙트럼 군집화에서 블록 대각 형태의 유사도 행렬 구성)

  • Heo, Gyeong-Yong;Kim, Kwang-Baek;Woo, Young-Woon
    • Journal of Korea Multimedia Society
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    • v.11 no.9
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    • pp.1302-1309
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    • 2008
  • Traditional clustering methods, like k-means or fuzzy clustering, are prototype-based methods which are applicable only to convex clusters. On the other hand, spectral clustering tries to find clusters only using local similarity information. Its ability to handle concave clusters has gained the popularity recent years together with support vector machine (SVM) which is a kernel-based classification method. However, as is in SVM, the kernel width plays an important role and has a great impact on the result. Several methods are proposed to decide it automatically, it is still determined based on heuristics. In this paper, we proposed an adaptive method deciding the kernel width based on distance histogram. The proposed method is motivated by the fact that the affinity matrix should be formed into a block diagonal matrix to generate the best result. We use the tradition Euclidean distance together with the random walk distance, which make it possible to form a more apparent block diagonal affinity matrix. Experimental results show that the proposed method generates more clear block structured affinity matrix than the existing one does.

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The properties of pad conditioning according to manufacturing methods of CMP pad conditioner (CMP 패드 컨디셔너의 제조공법에 따른 패드 컨디셔닝 특성)

  • Kang S.K.;Song M.S.;Jee W.H.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2005.10a
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    • pp.362-365
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    • 2005
  • Currently Chemical Mechanical Planarization (CMP) has become an essential step in the overall semiconductor wafer fabrication technology. Especially the CMP pad conditioner, one of the diamond tools, is required to have strong diamond retention. Strong cohesion between diamond grits and metal matrix prevents macro scratch on the wafer. If diamond retention is weak, the diamond will be pulled out of metal matrix. The pulled diamond grits are causative of macro scratch on wafer during CMP process. Firstly, some results will be reported of cohesion between diamond grits and metal matrix on the diamond tools prepared by three different manufacturing methods. A measuring instrument with sharp cemented carbide connected with a push-pull gauge was manufactured to measure the cohesion between diamond grits and metal matrix. The retention force of brazed diamond tool was stronger than the others. The retention force was also increased in proportion to the contact area of diamond grits and metal matrix. The brazed diamond tool has a strong chemical combination of the interlayer composed of chrome in metal matrix and carbon which enhance the interfacial cohesion strength between diamond grits and metal matrix. Secondly, we measured real-time data of the coefficient of friction and the pad wear rate by using CMP tester (CETR, CP-4). CMP pad conditioner samples were manufactured by brazed, electro-plated and sintered methods. The coefficient of friction and the pad wear rate were shown differently according to the arranged diamond patterns. Consequently, the coefficient of friction is increased according as the space between diamonds is increased or the concentration of diamonds is decreased. The pad wear rate is increased according as the degree of diamond protrusion is increased.

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Design of FIR/IIR Lattice Filters using the Circulant Matrix Factorization (Circulant Matrix Factorization을 이용한 FIR/IIR Lattice 필터의 설계)

  • Kim Sang-Tae;Lim Yong-Kon
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.41 no.1
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    • pp.35-44
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    • 2004
  • We Propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used for spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR filter and for the case of the In filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

Document Clustering Method using Coherence of Cluster and Non-negative Matrix Factorization (비음수 행렬 분해와 군집의 응집도를 이용한 문서군집)

  • Kim, Chul-Won;Park, Sun
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.13 no.12
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    • pp.2603-2608
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    • 2009
  • Document clustering is an important method for document analysis and is used in many different information retrieval applications. This paper proposes a new document clustering model using the clustering method based NMF(non-negative matrix factorization) and refinement of documents in cluster by using coherence of cluster. The proposed method can improve the quality of document clustering because the re-assigned documents in cluster by using coherence of cluster based similarity between documents, the semantic feature matrix and the semantic variable matrix, which is used in document clustering, can represent an inherent structure of document set more well. The experimental results demonstrate appling the proposed method to document clustering methods achieves better performance than documents clustering methods.

Speed-up of the Matrix Computation on the Ridge Regression

  • Lee, Woochan;Kim, Moonseong;Park, Jaeyoung
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.15 no.10
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    • pp.3482-3497
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    • 2021
  • Artificial intelligence has emerged as the core of the 4th industrial revolution, and large amounts of data processing, such as big data technology and rapid data analysis, are inevitable. The most fundamental and universal data interpretation technique is an analysis of information through regression, which is also the basis of machine learning. Ridge regression is a technique of regression that decreases sensitivity to unique or outlier information. The time-consuming calculation portion of the matrix computation, however, basically includes the introduction of an inverse matrix. As the size of the matrix expands, the matrix solution method becomes a major challenge. In this paper, a new algorithm is introduced to enhance the speed of ridge regression estimator calculation through series expansion and computation recycle without adopting an inverse matrix in the calculation process or other factorization methods. In addition, the performances of the proposed algorithm and the existing algorithm were compared according to the matrix size. Overall, excellent speed-up of the proposed algorithm with good accuracy was demonstrated.