• 대한수학회지
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• 제61권3호
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• pp.427-444
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• 2024

The matrix completion problem is to predict missing entries of a data matrix using the low-rank approximation of the observed entries. Typical approaches to matrix completion problem often rely on thresholding the singular values of the data matrix. However, these approaches have some limitations. In particular, a discontinuity is present near the thresholding value, and the thresholding value must be manually selected. To overcome these difficulties, we propose a shrinkage and thresholding function that smoothly thresholds the singular values to obtain more accurate and robust estimation of the data matrix. Furthermore, the proposed function is differentiable so that the thresholding values can be adaptively calculated during the iterations using Stein unbiased risk estimate. The experimental results demonstrate that the proposed algorithm yields a more accurate estimation with a faster execution than other matrix completion algorithms in image inpainting problems.

• 충청수학회지
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• 제16권1호
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• pp.25-36
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• 2003

We study the question of whether a partial (0, 1)-normal matrix has a non-symmetric normal completion. Matrix sandwich problems are an important and special case of matrix completion problems. In this paper, we give some properties for the (0, 1)-normal matrices and some large classes that satisfies the normal sandwich completion.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권7호
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• pp.3057-3075
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• 2020

End-to-end network delay plays an vital role in distributed services. This delay is used to measure QoS (Quality-of-Service). It would be beneficial to know all node-pair delay information, but unfortunately it is not feasible in practice because the use of active probing will cause a quadratic growth in overhead. Alternatively, using the measured network delay to estimate the unknown network delay is an economical method. In this paper, we adopt the state-of-the-art matrix completion technology to better estimate the network delay from limited measurements. Although the number of measurements required for an exact matrix completion is theoretically bounded, it is practically less helpful. Therefore, we propose an online adaptive sampling algorithm to measure network delay in which statistical leverage scores are used to select potential matrix elements. The basic principle behind is to sample the elements with larger leverage scores to keep the traits of important rows or columns in the matrix. The amount of samples is adaptively decided by a proposed stopping condition. Simulation results based on real delay matrix show that compared with the traditional sampling algorithm, our proposed sampling algorithm can provide better performance (smaller estimation error and less convergence pressure) at a lower cost (fewer samples and shorter processing time).

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2015년도 추계학술대회
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• pp.4-7
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• 2015

In this paper, we propose a matrix completion algorithm for Internet of Things (IoT) localization. The proposed algorithm recovers the Gram matrix of sensors by performing optimization over the Riemannian manifold of fixed-rank positive semidefinite matrices. We compute and show the closed forms of all the differentially geometric components required for applying nonlinear conjugate gradients combined with Armijo line search method. The numerical experiments show that the performance of the proposed algorithm in solving IoT localization is outstanding compared with the state-of-the-art matrix completion algorithms both in noise and noiseless scenarios.

• 정보처리학회논문지A
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• 제9A권3호
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• pp.371-378
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• 2002

EMFG(Extended Mark Flow Graph)는 이산시스템을 표현하는데 유용한 그래프 도구로 알려져 있다. 본 연구에서는 EMFG에서 각 트랜지션이 점화하였을 때의 입출력 박스의 마크 변화량을 입출력 행렬로 표현하였고, 이를 사용하여 EMFG의 접속행렬을 구하였다. 점화가능벡터를 구하기 위하여 각 트랜지션의 점화조건을 점화조건행렬로 표현하였으며, 각 트랜지션의 점화완료 상태를 판단하기 위하여 점화완료벡터를 도입하였다. 이들을 사용하여 EMFG의 모든 동작과정이 수학적으로 해석될 수 있도록 EMFG의 동작해석 알고리즘을 개선하였다. 제안된 알고리즘을 정회전과 역회전을 반복하는 시스템에 적용하여 알고리즘이 올바르게 동작하는 것을 확인하였다. 제안된 알고리즘은 다양한 이산 시스템을 분석하는데 유용하다.

• 대한수학회지
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• 제52권5호
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• pp.1003-1021
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• 2015

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

• 충청수학회지
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• 제24권3호
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• pp.587-593
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• 2011

We find concrete necessary and sufficient conditions for the existence of contractive completions of Stochastic Hankel partial contractions of size $4{\times}4$, extremal type.

• 대한수학회지
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• 제57권3호
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• pp.641-653
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• 2020

To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: $${\max}\{X:X=X^*,\;\(\array{A&V&X\\V&B&W\\X&W&C}\){\geq}0\}$$. We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.

• 한국통신학회논문지
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• 제42권3호
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• pp.604-611
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• 2017

무선 센서 네트워크에서 센서 노드는 제한된 전력을 사용하기 때문에 에너지 사용을 효율적으로 하는 것이 중요하다. 본 논문에서는 에너지사용효율을 높이기 위해 일정지역에서 측정되는 센서 값으로 이루어진 행렬이 low rank일 때 Matrix Completion을 이용하여 패킷 생성량을 줄이고, 센서가 측정값에 대응시킨 time slot으로 센서 ID 전송을 시도할 때 확률밀도함수로 예측한 전송 성공 확률에 따라 전송을 결정하여 overhead와 충돌을 줄이는 방법을 제안한다. 전산 모의실험을 통해 CSMA/CA와 비교하여 제안된 방법이 전송 실패 수가 17% 감소하고 패킷 생성량은 73%로 감소함을 보였다. 또한 CSMA/CA에 비해 시간 지연이 22%로 감소하고 fusion center에서 Singular Value Thresholding(SVT)로 센서 값을 복원한 경우 MSE error가 CSMA/CA에 비해 86%로 낮음을 보였다.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.157-163
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• 2014

For a finite subset ${\Lambda}$ of $\mathbb{N}_0{\times}\mathbb{N}_0$, where $\mathbb{N}_0$ is the set of nonnegative integers, we say that a complex data ${\gamma}_{\Lambda}:=\{{\gamma}_{ij}\}_{(ij){\in}{\Lambda}}$ in the unit disc $\mathbf{D}$ of complex numbers has a cyclic subnormal completion if there exists a Hilbert space $\mathcal{H}$ and a cyclic subnormal operator S on $\mathcal{H}$ with a unit cyclic vector $x_0{\in}\mathcal{H}$ such that ${\langle}S^{*i}S^jx_0,x_0{\rangle}={\gamma}_{ij}$ for all $i,j{\in}\mathbb{N}_0$. In this note, we obtain some sufficient conditions for a cyclic subnormal completion of ${\gamma}_{\Lambda}$, where ${\Lambda}$ is a finite subset of $\mathbb{N}_0{\times}\mathbb{N}_0$.