• Journal of the Korean Mathematical Society
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• v.61 no.3
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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.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.4
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• pp.145-155
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• 2015

Noise reduction has been actively studied in the digital image processing and recently, block-based denoising algorithms are widely used. In particular, a low rank approximation employing WNNM(Weighted Nuclear Norm Minimization) and block-based approaches demonstrated the potential for effective noise reduction. However, the algorithm based on low rank a approximation generates the artifacts in the image restoration step. In this paper, we analyzes the image content using the STFT(Short Time Fourier Transform) and proposes an effective method of minimizing the artifacts generated from the conventional algorithm. To evaluate the performance of the proposed scheme, we use the test images containing a wide range of noise levels and compare the results with the state-of-art algorithms.

• Journal of the Korea Society of Computer and Information
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• v.26 no.7
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• pp.1-7
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• 2021

In this paper, we propose a feature selection technique for multi-label classification. Many existing feature selection techniques have selected features by calculating the relation between features and labels such as a mutual information scale. However, since the mutual information measure requires a joint probability, it is difficult to calculate the joint probability from an actual premise feature set. Therefore, it has the disadvantage that only a few features can be calculated and only local optimization is possible. Away from this regional optimization problem, we propose a feature selection technique that constructs a low-rank space in the entire given feature space and selects features with sparsity. To this end, we designed a regression-based objective function using Nuclear norm, and proposed an algorithm of gradient descent method to solve the optimization problem of this objective function. Based on the results of multi-label classification experiments on four data and three multi-label classification performance, the proposed methodology showed better performance than the existing feature selection technique. In addition, it was showed by experimental results that the performance change is insensitive even to the parameter value change of the proposed objective function.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.12
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• pp.56-65
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• 2001

This paper proposes an algorithm for the capacitance extraction of general 3-dimensional conductors in an ideal uniform dielectric that uses a high-order quadrature approximation method combined with the typical first-order collocation method to enhance the accuracy and adopts an efficient matrix-vector product algorithm for the model-order reduction to achieve efficiency. The proposed method enhances the accuracy using the quadrature method for interconnects containing corners and vias that concentrate the charge density. It also achieves the efficiency by reducing the model order using the fact that large parts of system matrices are of numerically low rank. This technique combines an SVD-based algorithm for the compression of rank-deficient matrices and Gram-Schmidt algorithm of a Krylov-subspace iterative technique for the rapid multiplication of matrices. It is shown through the performance evaluation procedure that the combination of these two techniques leads to a more efficient algorithm than Gaussian elimination or other standard iterative schemes within a given error tolerance.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.2
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• pp.18-26
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• 1992

MR(Model Reduction) is presented in order to estimate the frequency of multiple sinusoids from the finite noisy data with the white or colored noises. MR, using the reduced rank models, is designed, appling the approximation of linear system to LP(Linear Prediction). The MR method is analyzed. Monte-carlo simulations are conducted for MR and Lp. The results are compared with in terms of mean, root-mean square and relative bias. MR eliminates effectevely the extremeous and exceptional poles appearing in LP and improves the accuracy of LP. Especially, MR gives promising results in short noisy measurements, low SNR's and colored noises. Power spectral density and angular frequency position are showed by figures, for examples. Finally, the new method is utilized to the communication and biomedical systems estimating the characteristics of the signal and the system identification modelling the dynamic systems from experimental data.

• Proceedings of the KOSOMBE Conference
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• v.1997 no.05
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• pp.184-187
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• 1997

In terms of a system identification, we present a method for autoregressive(AR) modelling of variious biomedical signal. Model order is estimated fly low rank approximation and coefficients are determined by innovation processes of Kalman filter derivation. An application of the method is given for visual evoked potentials.

• ETRI Journal
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• v.40 no.4
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• pp.421-434
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• 2018

The application of deep neural networks (DNNs) to connect the world with cyber physical systems (CPSs) has attracted much attention. However, DNNs require a large amount of memory and computational cost, which hinders their use in the relatively low-end smart devices that are widely used in CPSs. In this paper, we aim to determine whether DNNs can be efficiently deployed and operated in low-end smart devices. To do this, we develop a method to reduce the memory requirement of DNNs and increase the inference speed, while maintaining the performance (for example, accuracy) close to the original level. The parameters of DNNs are decomposed using a hybrid of canonical polyadic-singular value decomposition, approximated using a tensor power method, and fine-tuned by performing iterative one-shot hybrid fine-tuning to recover from a decreased accuracy. In this study, we evaluate our method on frequently used networks. We also present results from extensive experiments on the effects of several fine-tuning methods, the importance of iterative fine-tuning, and decomposition techniques. We demonstrate the effectiveness of the proposed method by deploying compressed networks in smartphones.

• Proceedings of the Acoustical Society of Korea Conference
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• autumn
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• pp.335-338
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• 2001

잔향음은 시변동성이 존재하는 유동성 경계면 잔향음(해수면, 체적)과 시변동성이 존재하지 않는 고정 경계면 잔향음(해저면)으로 분류된다. 그러나 고정 경계면 잔향음으로 알려진 해저면 잔향음에서도 단주기적 시변동성이 존재하고 있음이 여러 실측자료에서 관측되고 있다. 본 연구는 시변동성의 원인을 파악하고자 실험실에서 부유성 퇴적물의 농토에 따른 후방산란 신호를 측정하였다. 또한 동해에서 측정된 시간에 따른 잔향음신호(80kHz)와 ADCP(4.2MHz) 자료를 비교하여 천해에서의 체적 산란체의 변동이 잔향음 신호에 영향을 미칠 수 있음을 확인하였다. 아울러 본 논문에서는 잔향음 신호의 단주기적 시변동성에 의한 잡음 성분을 제거하여 표준화된 잔향음 신호를 획득하기 위한 방법으로 Low Rank Approximation(LRA)을 제안하였다. 이 기법은 특이해 분해(Singular Value Decomposition, SVD)를 수행하여 실측 자료 행렬로부터 고유치(Eigenvalue)과 고유벡터(Eigenvector)를 추출한 후, 추출된 고유치를 제한적으로 사용하여 근사화 하는 기법으로 시변동성 신호를 제거하는데 효율적인 방법이다.