• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.3
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• pp.437-447
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• 2003

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 fur 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 Inter and for the case of the IIR filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

• International Journal of Control, Automation, and Systems
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• v.6 no.3
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• pp.378-385
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• 2008

This paper aims to present a polynomial approach to the steady-state optimal filtering for delayed systems. The design of the steady-state filter involves solving one polynomial equation and one spectral factorization. The key problem in this paper is the derivation of spectral factorization for systems with delayed measurement, which is more difficult than the standard systems without delays. To get the spectral factorization, we apply the reorganized innovation approach. The calculation of spectral factorization comes down to two Riccati equations with the same dimension as the original systems.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.359-373
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• 2012

The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.

• 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).

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.495-509
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• 2002

We propose variants of the modified incomplete Cho1esky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

• International Journal of Control, Automation, and Systems
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• v.1 no.2
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• pp.206-209
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• 2003

An $H_2$/$H_{\infty}$ -controller realization is carried out by considering an entropy integral. Using J-spectral factorization, the parametrizations of all $H_{\infty}$ stabilizing controllers are derived. By the relation of a mixed $H_2$/$H_{\infty}$ control problem and a minimum entropy/$H_{\infty}$ control problem, the mixed $H_2$/$H_{\infty}$-controller state-space realization is presented.

• ETRI Journal
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• v.39 no.1
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• pp.21-29
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• 2017

This paper addresses the problem of unsupervised speech separation based on robust non-negative matrix factorization (RNMF) with ${\beta}$-divergence, when neither speech nor noise training data is available beforehand. We propose a robust version of non-negative matrix factorization, inspired by the recently developed sparse and low-rank decomposition, in which the data matrix is decomposed into the sum of a low-rank matrix and a sparse matrix. Efficient multiplicative update rules to minimize the ${\beta}$-divergence-based cost function are derived. A convolutional extension of the proposed algorithm is also proposed, which considers the time dependency of the non-negative noise bases. Experimental speech separation results show that the proposed convolutional RNMF successfully separates the repeating time-varying spectral structures from the magnitude spectrum of the mixture, and does so without any prior training.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.11
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• pp.58-66
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• 2001

GPC has been reported as a useful self-tuning control algorithm for systems with unknown time-delay and parameters. GPC is easy to understand and implement, and thus has won popularity among many practicing engineers. Despite its success, GPC does not guarantee is nominal stability. So, in this paper, GPC is rederived in frequency domain instead of in the time domain to guarantee its nominal stability. Derivation of GPC in frequency domain involves spectral factorization and Diophantine equation. Frequency domain GPC control law is stable because the zeros of characteristic polynomial are strictly Schur. Recursive least square algorithm is used to identify unknown parameters. To see the effectiveness of the proposed controller, the controller is simulated for a numerical problem that changes in dead-time, in order and in parameters.

• Proceedings of the Korean Society for Language and Information Conference
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• 2007.11a
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• pp.430-439
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• 2007

In this paper, we use non-negative matrix factorization (NMF) to refine the document clustering results. NMF is a dimensional reduction method and effective for document clustering, because a term-document matrix is high-dimensional and sparse. The initial matrix of the NMF algorithm is regarded as a clustering result, therefore we can use NMF as a refinement method. First we perform min-max cut (Mcut), which is a powerful spectral clustering method, and then refine the result via NMF. Finally we should obtain an accurate clustering result. However, NMF often fails to improve the given clustering result. To overcome this problem, we use the Mcut object function to stop the iteration of NMF.

• Journal of KIISE:Computing Practices and Letters
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• v.14 no.5
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• pp.497-501
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• 2008

In this paper we present a method for continuous EEG classification, where we employ nonnegative tensor factorization (NTF) to determine discriminative spectral features and use the Viterbi algorithm to continuously classily multiple mental tasks. This is an extension of our previous work on the use of nonnegative matrix factorization (NMF) for EEG classification. Numerical experiments with two data sets in BCI competition, confirm the useful behavior of the method for continuous EEG classification.