• Journal of Korean Society of Disaster and Security
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• v.8 no.1
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• pp.15-19
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• 2015

In rainfall-runoff models employed in hydrological applications, runoff amount is estimated through temporal delay of effective precipitation based on a linear system. Its amount is resulted from the linearized ratio by analyzing the convolution multiplier. Furthermore, in case of kernel density estimate (KDE) used in probabilistic analysis, the definition of the kernel comes from the convolution multiplier. Individual data values are smoothed through the kernel to derive KDE. In the current study, the roles of the convolution multiplier for KDE and rainfall-runoff models were revisited and their similarity and dissimilarity were investigated to discover the mathematical applicability of the convolution multiplier.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.515-526
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• 2021

Denote by ��+ the set of probability measures supported on ℝ+. Suppose V�� is the variance function of the Cauchy-Stieltjes Kernel (CSK) family ��-(��) generated by a non degenerate probability measure �� ∈ ��+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ${\nu}{\mapsto}{\mathbb{M}}_t({\nu})=({\nu}^{{\boxtimes}(t+1)})^{{\uplus}{\frac{1}{t+1}}}$ from ��+ onto itself.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.454-458
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• 2001

Based on a fuzzy system representation of gray scale images, we derive and edge detection algorithm whose convolution kernel is different from the known kernels such as those of Robert's Prewitt's or Sobel's gradient. Our fuzzy system representation is an exact representation of the bicubic spline function which represents the gray scale image approximately. Hence the fuzzy system is a continuous function and it provides a natural way to define the gradient and the Laplacian operator. We show that the gradient at grid points can be evaluated by taking the convolution of the image with a 3$\times$3 kernel. We also that our gradient coupled with the approximate value of the continuous function generates an edge detection method which creates edge images clearer than those by other methods. A few examples of applying our methods are included.

• Journal of IKEEE
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• v.25 no.4
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• pp.664-671
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• 2021

This paper proposes a GPGPU structure that can reduce the number of operations and memory access by effectively applying a data reuse method to a convolutional neural network(CNN). Convolution is a two-dimensional operation using kernel and input data, and the operation is performed by sliding the kernel. In this case, a reuse method using an internal register is proposed instead of loading kernel from a cache memory until the convolution operation is completed. The serial operation method was applied to the convolution to increase the effect of data reuse by using the principle of GPGPU in which instructions are executed by the SIMT method. In this paper, for register-based data reuse, the kernel was fixed at 4×4 and GPGPU was designed considering the warp size and register bank to effectively support it. To verify the performance of the designed GPGPU on the CNN, we implemented it as an FPGA and then ran LeNet and measured the performance on AlexNet by comparison using TensorFlow. As a result of the measurement, 1-iteration learning speed based on AlexNet is 0.468sec and the inference speed is 0.135sec.

• Journal of the Korea Society of Computer and Information
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• v.26 no.4
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• pp.29-37
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• 2021

In this paper, we propose a deep learning-based retinal vessel segmentation model for handling multi-scale information of fundus images. we integrate the selective kernel convolution into U-Net-based convolutional neural network. The proposed model extracts and segment features information with various shapes and sizes of retinal blood vessels, which is important information for diagnosing eye-related diseases from fundus images. The proposed model consists of standard convolutions and selective kernel convolutions. While the standard convolutional layer extracts information through the same size kernel size, The selective kernel convolution extracts information from branches with various kernel sizes and combines them by adaptively adjusting them through split-attention. To evaluate the performance of the proposed model, we used the DRIVE and CHASE DB1 datasets and the proposed model showed F1 score of 82.91% and 81.71% on both datasets respectively, confirming that the proposed model is effective in segmenting retinal blood vessels.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.419-426
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• 2009

In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.

• ETRI Journal
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• v.39 no.6
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• pp.841-850
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• 2017

We investigate neural network image reconstruction for magnetic particle imaging. The network performance strongly depends on the convolution effects of the spectrum input data. The larger convolution effect appearing at a relatively smaller nanoparticle size obstructs the network training. The trained single-layer network reveals the weighting matrix consisting of a basis vector in the form of Chebyshev polynomials of the second kind. The weighting matrix corresponds to an inverse system matrix, where an incoherency of basis vectors due to low convolution effects, as well as a nonlinear activation function, plays a key role in retrieving the matrix elements. Test images are well reconstructed through trained networks having an inverse kernel matrix. We also confirm that a multi-layer network with one hidden layer improves the performance. Based on the results, a neural network architecture overcoming the low incoherence of the inverse kernel through the classification property is expected to become a better tool for image reconstruction.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.935-952
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• 2017

It is natural to try to find a kernel such that its convolution of integrable functions converges faster than that of the $Fej{\acute{e}}r$ kernel. In this paper, we introduce a weighted Fourier partial sums which are written as the convolution of signed good kernels and prove that the weighted Fourier partial sum converges in $L^2$ much faster than that of the $Ces{\grave{a}}ro$ means. In addition, we present two numerical experiments.

• Proceedings of the Korean Society for Language and Information Conference
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• 2007.11a
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• pp.415-421
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• 2007

This paper proposes a convolution tree kernel-based approach for relation extraction where the parse tree is expanded with entity features such as entity type, subtype, and mention level etc. Our study indicates that not only can our method effectively capture both syntactic structure and entity information of relation instances, but also can avoid the difficulty with tuning the parameters in composite kernels. We also demonstrate that predicate verb information can be used to further improve the performance, though its enhancement is limited. Evaluation on the ACE2004 benchmark corpus shows that our system slightly outperforms both the previous best-reported feature-based and kernel-based systems.

• The KIPS Transactions:PartB
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• v.13B no.1 s.104
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• pp.27-34
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• 2006

In this study, we propose this new algorithm that generates score function in ICA(Independent Component Analysis) using entropy theory. To generate score function, estimation of probability density function about original signals are certainly necessary and density function should be differentiated. Therefore, we used kernel density estimation method in order to derive differential equation of score function by original signal. After changing formula to convolution form to increase speed of density estimation, we used FFT algorithm that can calculate convolution faster. Proposed score function generation method reduces the errors, it is density difference of recovered signals and originals signals. In the result of computer simulation, we estimate density function more similar to original signals compared with Extended Infomax and Fixed Point ICA in blind source separation problem and get improved performance at the SNR(Signal to Noise Ratio) between recovered signals and original signal.