• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.33.5-33
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• 2001

We consider here the problem of spectral estimation of multidimensional wide sense stationary (WSS) random process. A method, employing a special difference equation of correlation function, is proposed to solve the problem of multidimensional spectral estimation. In this approach, the special difference equation of correlation function is derived by modal decomposition method. Maximum likelihood estimator and Kalman filter are used to estimate the model parameters of the difference equation and the decomposed spectral residues. An algorithm is presented to estimate the multidimensional spectral density. According to the result of the simulation, these methods are feasible to estimate the spectral density of WSS process, which is realized by finite dimensional multivariable lineal system driven by white noise.

• 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.

• 대한의용생체공학회:의공학회지
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• 제16권4호
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• pp.395-402
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• 1995

자기공명 영상 시스템에서 영상을 얻고자 하는 물체내의 자화율 차이는 복셀내의 스핀들의 위상을 변화시킨다. 또한 스핀들 상호간의 위상변화로 인하여 영상 신호는 감쇄된다. 이러한 신호 세기의 감쇄는 자기공명 영상분야에서 자화율 효과라 알려져 왔고 이런 효과를 억제시키거나 또는 이용하는 연구가 심도있게 논의되어왔다. 본 논문에서 자화율 효과로 인한 신호의 변화를 분석할 수 있는 새로운 스펙트럼 분해법과 영상법을 제안하였다. 그리고 자화율 스펙트럼 분해법을 위한 펄스시퀀스를 개발하였고, 이것을 상자성(paramagnetic) 성질 때문에 자화율 효과가 생기는 정맥영상에 적용하였다. 컴퓨터 모의 실험과 팬텀(phantom)을 대상으로 한 실험 결과로 스펙트럼 분해법의 타당성을 보였다.

• 대한수학회지
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• 제57권4호
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• pp.935-955
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• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

• 대한의용생체공학회:의공학회지
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• 제8권1호
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• pp.69-74
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• 1987

The power spectrum of background EEG is estimated by the Plsarenko Harmonic Decomposition with the stochastic process whlch consists of the nonhamonic sinus Bid and the white nosie. The estimation results are examined and compared with the results from the maximum entropy spectral extimation, and the optimal order of this from the maximum entropy spectral extimation, and the optimal order of this model can be determined from the eigen value's fluctuation of autocorrelation of background EEG. From the comparing results, this method is possible to estimate the power spectrum of background EEG.

• 응용통계연구
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• 제22권3호
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• pp.499-513
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• 2009

An economic signal in the real world usually reflects complex phenomena. One may have difficulty both extracting and interpreting information embedded in such a signal. A natural way to reduce complexity is to decompose the original signal into several simple components, and then analyze each component. Spectral analysis (Priestley, 1981) provides a tool to analyze such signals under the assumption that the time series is stationary. However when the signal is subject to non-stationary and nonlinear characteristics such as amplitude and frequency modulation along time scale, spectral analysis is not suitable. Huang et al. (1998b, 1999) proposed a data-adaptive decomposition method called empirical mode decomposition and then applied Hilbert spectral analysis to decomposed signals called intrinsic mode function. Huang et al. (1998b, 1999) named this two step procedure the Hilbert-Huang transform(HHT). Because of its robustness in the presence of nonlinearity and non-stationarity, HHT has been used in various fields. In this paper, we discuss the applications of the HHT and demonstrate its promising potential for non-stationary financial time series data provided through a Korean stock price index.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2005년도 한국컴퓨터종합학술대회 논문집 Vol.32 No.1 (A)
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• pp.892-894
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• 2005

Graph partitioning provides an important tool for data clustering, but is an NP-hard combinatorial optimization problem. Spectral clustering where the clustering is performed by the eigen-decomposition of an affinity matrix [1,2]. This is a popular way of solving the graph partitioning problem. On the other hand, semidefinite relaxation, is an alternative way of relaxing combinatorial optimization. issuing to a convex optimization[4]. In this paper we present a semidefinite programming (SDP) approach to graph equi-partitioning for clustering and then we use eigen-decomposition to obtain an optimal partition set. Therefore, the method is referred to as semidefinite spectral clustering (SSC). Numerical experiments with several artificial and real data sets, demonstrate the useful behavior of our SSC. compared to existing spectral clustering methods.

• Journal of the Korean Statistical Society
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• 제22권2호
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• 대한수학회보
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• 제51권2호
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• pp.387-400
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• 2014

We prove that the set of k-type nonwandering points of a Z2-action T can be decomposed into a disjoint union of closed and T-invariant sets $B_1,{\ldots},B_l$ such that $T|B_i$ is topologically k-type transitive for each $i=1,2,{\ldots},l$, if T is expansive and has the shadowing property.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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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.