• 한국정보통신학회논문지
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• 제15권2호
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• pp.364-370
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• 2011

본 논문은 공분산 행렬과 리만 다양체 이론에 근거를 둔 이동물체를 추적하는 새로운 방법을 제안한다. 연속적으로 변화하는 동영상 배경에서 다양한 변형을 겪는 비정형 물체를 추적하기 위해 공분산 행렬을 사용하여 특징 추출을 한다. 공분산 행렬은 특징들의 상관관계뿐만 아니라 공간적인 속성과 통계학적인 속성을 다룰 수 있으므로 서로 다른 유형의 특징들의 융합이 가능하며 행렬의 차원이 작다. 그러므로 이동물체 영역의 공분산 행렬을 특징벡터로 구성하고 후보 영역의 공분산 행렬과 비교 연산함으로써 각 프레임마다 이동물체의 위치를 추정할 수 있다. 여기서 리만 기하학은 이동물체의 변형과 모양 변화에 효과적으로 적용될 수 있으며 최소 거리를 갖는 추정 영역을 계산하기 위해 측지선 거리를 사용하므로 정확도를 향상시킨다. 제안한 방법의 효율성은 실험을 통해 검증하였다.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.361-370
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• 2001

Testing equality of covariance matrix of k populations has long been an interesting issue in statistical inference. To overcome the sparseness of data points in a high-dimensional space and deal with the general cases, we suggest several projection pursuit type statistics. Some results on the limiting distributions of the statistics are obtained. some properties of Bootstrap approximation are investigated. Furthermore, for computational reasons an approximation which is based on Number theoretic method for the statistics is adopted. Several simulation experiments are performed.

• ETRI Journal
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• 제40권5호
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• pp.634-642
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• 2018

Projection spectral analysis is investigated and refined in this paper, in order to unify principal component analysis and independent component analysis. Singular value decomposition and spectral theorems are applied to nonsymmetric correlation or covariance matrices with multiplicities or singularities, where projections and nilpotents are obtained. Therefore, the suggested approach not only utilizes a sum-product of orthogonal projection operators and real distinct eigenvalues for squared singular values, but also reduces the dimension of correlation or covariance if there are multiple zero eigenvalues. Moreover, incremental learning strategies of projection spectral analysis are also suggested to improve the performance.

• ETRI Journal
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• 제45권3호
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• pp.492-504
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• 2023

Researchers have recently shown an increased interest in estimating the direction-of-arrival (DOA) of wideband noncircular sources, but existing studies have been restricted to subspace-based methods. An off-grid sparse recovery-based algorithm is proposed in this paper to improve the accuracy of existing algorithms in low signal-to-noise ratio situations. The covariance and pseudo covariance matrices can be jointly represented subject to block sparsity constraints by taking advantage of the joint sparsity between signal components and bias. Furthermore, the estimation problem is transformed into a single measurement vector problem utilizing the focused operation, resulting in a significant reduction in computational complexity. The proposed algorithm's error threshold and the Cramer-Rao bound for wideband noncircular DOA estimation are deduced in detail. The proposed algorithm's effectiveness and feasibility are demonstrated by simulation results.

• Journal of the Korean Data and Information Science Society
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• 제10권2호
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• pp.369-385
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• 1999

성장곡선모형에서 다중 이상값들이나 영향관측값들을 탐지하는 문제는 선형회귀모형에서의 문제에 비해 매우 복잡하여 거의 이루어지지 않고 있는 실정이다. 본 연구에서는 이상점을 포함하고 있는 성장곡선모형에서 이들을 탐지하는 방법으로 평균이동모형을 이용하는 방법을 소개하였다. 이 방법을 이용하여 찾아낸 자료가 이상점인지의 여부를 예측표본재이용 의사 베이즈 우도 기준법을 이용한 등분산성의 검정을 통해 알아보았다. 끝으로 Potthoff(1964)등이 사용한 자료를 이용한 예제를 통해 이상점 탐지와 등분 산성 검정을 실시한 결과를 제시하였다.

• 한국산학기술학회논문지
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• 제6권4호
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• pp.291-295
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• 2005

본 논문은 변형된 2-D PCA를 이용한 얼굴 인식 방법에 대하여 제안한다. 기존의 PCA는 1 차원 벡터들로 공분산 행렬을 구하는 반면에 2-D PCA는 2 차원 영상을 직접적으로 이용하여 공분산 행렬을 구한 후 그것의 고유값에 따른 고유벡터를 구하여 특징 벡터들을 추출한다. 제안 방법은 두 개의 공분산 행렬들을 이용하여 선형 변환 행렬을 구하는 변형된 2-D PCA 방법을 적용하여 얼굴을 인식한다. 실험 결과는 2-D PCA 보다 제안된 방법이 $1\%$ 정도 얼굴 인식률이 더 좋으며, 안정된 인식률을 보여준다.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.515-521
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• 2010

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_n\;=\;\frac{1}{N}Y_nY_n^TT_n$ where $Y_n\;=\;[Y_{ij}]_{n\;{\times}\;N}$ is with independent, identically distributed entries and $T_n$ is an $n\;{\times}\;n$ symmetric non-negative definite random matrix independent of the $Y_{ij}$'s. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of $B_n$ has a continuous density function away from zero.

• 충청수학회지
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• 제22권3호
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• pp.519-524
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• 2009

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_{n}\;=\;\frac{1}{n}Y_{m}^{T}T_{m}Y_{m}$ where $Ym\;=\;[Y_{ij}]_{m{\times}n}$ is with independent, identically distributed entries and $T_m$ is an $m{\times}m$ symmetric nonnegative definite random matrix independent of the $Y_{ij}{^{\prime}}s$. In the present paper, using the inversion formula of the Stieltjes transform, we will find the density function of the limiting distribution of $B_n$ away from zero.

• East Asian mathematical journal
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• 제5권1호
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• pp.95-110
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• 1989

In a general variance component model, nonnegative quadratic estimators of the components of variance are considered which are invariant with respect to mean value translaion and have minimum bias (analogously to estimation theory of mean value parameters). Here the minimum is taken over an appropriate cone of positive semidefinite matrices, after having made a reduction by invariance. Among these estimators, which always exist the one of minimum norm is characterized. This characterization is achieved by systems of necessary and sufficient condition, and by a cone restricted pseudoinverse. In models where the decomposing covariance matrices span a commutative quadratic subspace, a representation of the considered estimator is derived that requires merely to solve an ordinary convex quadratic optimization problem. As an example, we present the two way nested classification random model. An unbiased estimator is derived for the mean squared error of any unbiased or biased estimator that is expressible as a linear combination of independent sums of squares. Further, it is shown that, for the classical balanced variance component models, this estimator is the best invariant unbiased estimator, for the variance of the ANOVA estimator and for the mean squared error of the nonnegative minimum biased estimator. As an example, the balanced two way nested classification model with ramdom effects if considered.

• Journal of the Korean Data and Information Science Society
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• 제20권4호
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• pp.757-764
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• 2009

In discriminant analysis, we consider a special pattern which contains a block of missing observations. We assume that the two populations are equally likely and the costs of misclassification are equal. In this situation, we consider the bootstrap confidence intervals of the error rate in the circular models when the covariance matrices are equal and not equal.