• Title/Summary/Keyword: Matrix decomposition

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Resistant h-Plot for a Sample Variance-Covariance Matrix

  • Park, Yong-Seok
    • 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.

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Projective Reconstruction from Multiple Images using Matrix Decomposition Constraints (행렬 분해 제약을 사용한 다중 영상에서의 투영 복원)

  • Ahn, Ho-Young;Park, Jong-Seung
    • Journal of Korea Multimedia Society
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    • v.15 no.6
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    • pp.770-783
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    • 2012
  • In this paper, we propose a novel structure recovery algorithm in the projective space using image feature points. We use normalized image feature coordinates for the numerical stability. To acquire an initial value of the structure and motion, we decompose the scaled measurement matrix using the singular value decomposition. When recovering structure and motion in projective space, we introduce matrix decomposition constraints. In the reconstruction procedure, a nonlinear iterative optimization technique is used. Experimental results showed that the proposed method provides proper accuracy and the error deviation is small.

Block Sparse Low-rank Matrix Decomposition based Visual Defect Inspection of Rail Track Surfaces

  • Zhang, Linna;Chen, Shiming;Cen, Yigang;Cen, Yi;Wang, Hengyou;Zeng, Ming
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.13 no.12
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    • pp.6043-6062
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    • 2019
  • Low-rank matrix decomposition has shown its capability in many applications such as image in-painting, de-noising, background reconstruction and defect detection etc. In this paper, we consider the texture background of rail track images and the sparse foreground of the defects to construct a low-rank matrix decomposition model with block sparsity for defect inspection of rail tracks, which jointly minimizes the nuclear norm and the 2-1 norm. Similar to ADM, an alternative method is proposed in this study to solve the optimization problem. After image decomposition, the defect areas in the resulting low-rank image will form dark stripes that horizontally cross the entire image, indicating the preciselocations of the defects. Finally, a two-stage defect extraction method is proposed to locate the defect areas. The experimental results of the two datasets show that our algorithm achieved better performance compared with other methods.

An Estimating Method for Priority Vector in AHP, Using the Eigen-Decomposition of a Skew-Symmetric Matrix (AHP에서 왜대칭행렬의 고유분해를 이용한 중요도 추정법의 제안)

  • 이광진
    • The Korean Journal of Applied Statistics
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    • v.17 no.1
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    • pp.119-134
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    • 2004
  • Generally to estimate the priority vector in AHP, an eigen-vector method or a log-arithmic least square method is applied to pairwise comparison matrix itself. In this paper an estimating method is suggested, which is applied to pairwise comparison matrix adjusted by using the eigen-decomposition of skew-symmetric matrix. We also show theoretical background, meanings, and several advantages of this method by example. This method may be useful in case that pairwise comparison matrix is quite inconsistent.

Comparison of the covariance matrix for general linear model (일반 선형 모형에 대한 공분산 행렬의 비교)

  • Nam, Sang Ah;Lee, Keunbaik
    • The Korean Journal of Applied Statistics
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    • v.30 no.1
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    • pp.103-117
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    • 2017
  • In longitudinal data analysis, the serial correlation of repeated outcomes must be taken into account using covariance matrix. Modeling of the covariance matrix is important to estimate the effect of covariates properly. However, It is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcome the restrictions, several Cholesky decomposition approaches for the covariance matrix were proposed: modified autoregressive (AR), moving average (MA), ARMA Cholesky decompositions. In this paper we review them and compare the performance of the approaches using simulation studies.

Application to the design of reduced-order robust MPC and MIMO identification

  • Lee, Kwang-Soon;Kim, Sang-Hoon
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.313-316
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    • 1997
  • Two different issues, design of reduced-order robust model predictive control and input signal design for identification of a MIMO system, are addressed and design techniques based on singular value decomposition(SVD) of the pulse response circulant matrix(PRCM) are proposed. For this, we investigate the properties of the PRCM, which is a periodic approximation of a linear discrete-time system, and show its SVD represents the directional as well as the frequency decomposition of the system. Usefulness of the PRCM and effectiveness of the proposed design techniques are demonstrated through numerical examples.

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An Orthogonal Representation of Estimable Functions

  • Yi, Seong-Baek
    • Communications for Statistical Applications and Methods
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    • v.15 no.6
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    • pp.837-842
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    • 2008
  • Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.

LEVEL-m SCALED CIRCULANT FACTOR MATRICES OVER THE COMPLEX NUMBER FIELD AND THE QUATERNION DIVISION ALGEBRA

  • Jiang, Zhao-Lin;Liu, San-Yang
    • Journal of applied mathematics & informatics
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    • v.14 no.1_2
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    • pp.81-96
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    • 2004
  • The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

On Computing a Cholesky Decomposition

  • Park, Jong-Tae
    • Communications for Statistical Applications and Methods
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    • v.3 no.2
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    • pp.37-42
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    • 1996
  • Maximum likelihood estimation of Cholesky decomposition is considered under normality assumption. It is shown that maximum liklihood estimation gives a Cholesky decomposition of the sample covariance matrix. The joint distribution of the maximum likelihood estimators is derived. The ussual algorithm for a Cholesky decomposition is shown to be equivalent to a maximumlikelihood estimation of a Cholesky root when the underlying distribution is a multivariate normal one.

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The Role of Inorganic Compounds Additions on the Matrix Microtexture Control of C/C Composite (무기화합물 첨가에 의한 C/C복합재료의 매트릭스 조직제어)

  • ;安田榮
    • Journal of the Korean Ceramic Society
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    • v.34 no.11
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    • pp.1151-1158
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    • 1997
  • Fracture of uni-directional carbon fiber reinforced carbon matrix composite is strongly dependent on the orientation of basal plane in graphite matrix when it is limited within matrix. The orientation of basal planes are vertically stacked to carbon fiber which results in the weakness for applied tensile or shear force in thermosetting resin derived-carbon matrix composite. Microtextural control of the matrix was tried through chemical interaction between metal carbides and furan resin derived-carbon matrix. SiC and TiO2 addition made the orientation disordered. However, porosity increased due to decomposition of SiC. Interfacial bonding could be controlled by TiO2 addition, but carbon fiber was considerably reacted with TiC during thermal treatment higher than 2$600^{\circ}C$. Therefore, it is desirable to control the thermal treatment temperature at which decomposition of SiC was not serious and TiC/C was not formed eutectoid.

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