• Journal of KIISE
• /
• v.43 no.8
• /
• pp.910-918
• /
• 2016

A tensor is a multi-dimensional array that represents many data such as (user, user, time) in the social network system. A tensor generator is an important tool for multi-dimensional data mining research with various applications including simulation, multi-dimensional data modeling/understanding, and sampling/extrapolation. However, existing tensor generators cannot generate sparse tensors like real-world tensors that obey power law. In addition, they have limitations such as tensor sizes that can be processed and additional time required to upload generated tensor to distributed systems for further analysis. In this study, we propose TeT, a distributed tera-scale tensor generator to solve these problems. TeT generates sparse random tensor as well as sparse R-MAT and Kronecker tensor without any limitation on tensor sizes. In addition, a TeT-generated tensor is immediately ready for further tensor analysis on the same distributed system. The careful design of TeT facilitates nearly linear scalability on the number of machines.

• Smart Media Journal
• /
• v.4 no.4
• /
• pp.18-23
• /
• 2015

In this paper, we propose a method for detecting the number of clusters. This method can improve the performance of a gaussian mixture model function in conventional markov random field method by using the tensor voting. The key point of the proposed method is that extracts the number of the center through the continuity of saliency map of the input data of the tensor voting token. At first, we separate the foreground and background region candidate in a given natural images. After that, we extract the appropriate cluster number for each separate candidate regions by applying the tensor voting. We can make accurate modeling a gaussian mixture model by using a detected number of cluster. We can return the result of natural binary text image by calculating the unary term and the pairwise term of markov random field. After the experiment, we can confirm that the proposed method returns the optimal cluster number and text binarization results are improved.

• Journal of the Korean Statistical Society
• /
• v.19 no.2
• /
• pp.105-112
• /
• 1990

Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $\hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(\hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{\infty}$ norms.

• Journal of the Korean Statistical Society
• /
• v.21 no.2
• /
• pp.153-166
• /
• 1992

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.

• Journal of the Korean Geotechnical Society
• /
• v.17 no.5
• /
• pp.71-82
• /
• 2001

불포화토에 있어서 함수상태는 지반이 건조할수록 수축하고 습윤상태로 진행할수록 파괴에 이르게 하는 추가적인 입자간 응력을 발생시키며, 이러한 간극수와 흙입자 사이에 발생하는 현상을 규명하기 위해서는 정확한 모형화가 필요하다. 흙입자와 간극수 사이의 상호작용에서 흡입유발 유효응력(suction-induced effective stress)을 규명하기 위해 정규모형(regular packing)과 임의모형(random packing)이 적용될 수 있다. 최근의 연구결과에 따르면 흙은 흡입유발 유효응력과 밀접한 관계가 있으며, 흙의 비등방텐서(anisotropic tensor)를 구하기 위해 적용된 ALTERNAT 모델을 이용하여 구조텐서(fabric tensor)를 개략적으로 정의할 수 있다. Thornton의 임의모형 시뮬레이션은 구조텐서에 상응하는 파괴응력 상태를 포함하고 있으며, 미소역학 시뮬레이션을 통하여 구조텐서를 구하였다. 본 연구에서는 상기에 언급된 구형의 흙입자 모형에 대한 이론적 고찰이 수행되었고, ALTERNAT 모델을 적용한 간단한 비등방텐서의 결과를 구조텐서와 비교하였다. 본 연구결과 비등방텐서는 미소역학 시뮬레이션에 의한 구조텐서에 비해 약 20~40%정도 큰 값을 나타내었다.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.221-231
• /
• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.28 no.3
• /
• pp.108-119
• /
• 2024

The Reynolds-averaged Navier-Stokes (RANS) simulations are commonly used in industrial applications due to their computational efficiency. However, the linear eddy viscosity model (LEVM) used in RANS often fails to accurately capture the anisotropy of Reynolds stress in complex flow conditions. To enhance RANS predictive accuracy, data-driven closure models, such as Tensor Basis Neural Network (TBNN) and Tensor Basis Random Forest (TBRF), have been proposed. However existing models, including TBNN and TBRF, have limitations in capturing the nonlocal patterns of turbulence models, resulting in irregular and unsmooth predictions. Convolutional neural networks (CNNs) are considered as an alternative approach, but their reliance on discretization poses challenges when dealing with arbitrarily designed meshes in RANS simulations. In this study, we propose a nonlinear convolutional neural operator as the RANS closure model. Our model satisfies Galilean invariance, can learn nonlocal physics, and recovers high-resolution physics even when trained on undersampled grids. The model outperforms existing TBNN and TBRF models, successfully predicting smooth fields of Reynolds stress in flows with adverse pressure gradients, separations, and streamline curvature, where existing models struggle or fail to provide accurate predictions.

• Korea-Australia Rheology Journal
• /
• v.19 no.1
• /
• pp.17-25
• /
• 2007

In liquid composite molding (LCM), composites are produced by impregnation of a dry preform with liquid resin. The resin flow through the preform is usually described by Darcy's law and the permeability tensor must be obtained for filling analysis. While the resin flow in the thickness direction can be neglected for thin parts, the resin flow in the transverse direction is important for thicker parts. However, the transverse permeability of the preform has not been investigated frequently. In this study, the transverse permeability was measured experimentally for five different fiber preforms. In order to verify the experimental results, the measured transverse permeability was compared with numerical results. Five different fiber mats were used in this study: glass fiber woven fabric, aramid fiber woven fabric, glass fiber random mat, glass fiber braided preform, and glass/aramid hybrid braided preform. The anisotropic braided preforms were manufactured by using a three dimensional braiding machine. The pressure was measured at the inlet and outlet positions with pressure transducers.

• KIPS Transactions on Software and Data Engineering
• /
• v.3 no.10
• /
• pp.421-428
• /
• 2014

Like Alzheimer's disease, Parkinson's Disease(PD) is one of the most common neurodegenerative brain disorders. PD results from the deterioration of dopaminergic neurons in the brain region called the substantia nigra. Currently there is no cure for PD, but diagnosing in its early stage is important to provide treatments for relieving the symptoms and maintaining quality of life. Unlike many diagnosis methods of PD which use a single biomarker, we developed a diagnosis method that uses both biochemical biomarkers and imaging biomarkers. Our method uses ${\alpha}$-synuclein protein levels in the cerebrospinal fluid and diffusion tensor images(DTI). It achieved an accuracy over 91.3% in the 10-fold cross validation, and the best accuracy of 72% in an independent testing, which suggests a possibility for early detection of PD. We also analyzed the characteristics of the brain fiber pathways of Parkinson's disease patients and normal elderly people.

• Journal of Biomedical Engineering Research
• /
• v.25 no.6
• /
• pp.439-445
• /
• 2004

Diffusion tensor image(DTI) exploits the random diffusional motion of water molecules. This method is useful for the characterization of the architecture of tissues. In some tissues, such as muscle or cerebral white matter, cellular arrangement shows a strongly preferred direction of water diffusion, i.e., the diffusion is anisotropic. The degree of anisotropy is often represented using diffusion anisotropy indices (relative anisotropy(RA), fractional anisotropy(FA), volume ratio(VR)). In this study, FA images were obtained using different gradient schemes(N=6, 11, 23, 35. 47). Mean values and the standard deviations of FA were then measured at several anatomic locations for each scheme. The results showed that both mean values and the standard deviations of FA were decreased as the number of gradient directions were increased. Also, the standard error of ADC measurement decreased as the number of diffusion gradient directions increased. In conclusion, different gradient schemes showed a significantly different noise performance and the schem with more gradient directions clearly improved the quality of the FA images. But considering acquisition time of image and standard deviation of FA, 23 gradient directions is clinically optimal.