• 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.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.59-72
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• 2005

We study convergence of symmetric multisplitting method associated with many different multisplittings for solving a linear system whose coefficient matrix is a symmetric positive definite matrix which is not an H-matrix.

• Journal of Korean Institute of Industrial Engineers
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• v.25 no.3
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• pp.290-297
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• 1999

In interior point methods for linear programming, we must solve a linear system with a symmetric positive definite matrix at every iteration, and Cholesky factorization is generally used to solve it. Therefore, if Cholesky factorization is not done successfully, many iterations are needed to find the optimal solution or we can not find it. We studied methods for improving the numerical stability of Cholesky factorization and the accuracy of the solution of the linear system.

• The KIPS Transactions:PartB
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• v.13B no.6 s.109
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• pp.625-632
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• 2006

Collaborative filtering is a technology that aims at teaming predictive models of user preferences. Collaborative filtering systems have succeeded in Ecommerce market but they have shortcomings of high dimensionality and sparsity. In this paper we propose the nearest neighbor collaborative filtering method using non-negative matrix factorization(NNMF). We replace the missing values in the user-item matrix by using the user variance coefficient method as preprocessing for matrix decomposition and apply non-negative factorization to the matrix. The positive decomposition method using the non-negative decomposition represents users as semantic vectors and classifies the users into groups based on semantic relations. We compute the similarity between users by using vector similarity and selects the nearest neighbors based on the similarity. We predict the missing values of items that didn't rate by a new user based on the values that the nearest neighbors rated items.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2002.11a
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• pp.189-190
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• 2002

PMF(Positive Matrix Factorization) 모텔은 기존의 인자분석 모델이 갖는 인자부하량의 음수 문제를 해결하기 위해 인자부하량과 공통인자를 양수로 제한하여 결과 해석에 명확성을 주었다. 또한 환경연구에서 많이 나타나는 outlier와 log-normal분포모형을 선택사항으로 도입하고 있어 현재 환경관련 연구에 응용성이 높다. 본 연구에서는 대전 1, 2 공단 지역의 PM 10 중 미량금속과 이온성분의 농도를 분석하고 PMF를 이용하여 오염원을 확인하고자 한다. (중략)

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2005.11a
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• pp.83-84
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• 2005

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2004.11a
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• pp.124-125
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• 2004

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.6
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• pp.2098-2114
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• 2021

Light intensity variation is one of the key factors which affect the accuracy of vehicle face re-identification, so in order to improve the robustness of vehicle face features to light intensity variation, a Nonnegative Matrix Factorization model with the constraint of image acquisition time difference is proposed. First, the original features vectors of all pairs of positive samples which are used for training are placed in two original feature matrices respectively, where the same columns of the two matrices represent the same vehicle; Then, the new features obtained after decomposition are divided into stable and variable features proportionally, where the constraints of intra-class similarity and inter-class difference are imposed on the stable feature, and the constraint of image acquisition time difference is imposed on the variable feature; At last, vehicle face matching is achieved through calculating the cosine distance of stable features. Experimental results show that the average False Reject Rate and the average False Accept Rate of the proposed algorithm can be reduced to 0.14 and 0.11 respectively on five different datasets, and even sometimes under the large difference of light intensities, the vehicle face image can be still recognized accurately, which verifies that the extracted features have good robustness to light variation.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.59-80
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• 2003

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2006.04a
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• pp.237-238
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• 2006