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

• Journal of KIISE
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• v.45 no.3
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• pp.280-287
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• 2018

Recently, the use of a recommendation system and tensor data analysis, which has high-dimensional data, is increasing, as they allow us to analyze the tensor and extract potential elements and patterns. However, due to the large size and complexity of the tensor, it needs to be decomposed in order to analyze the tensor data. While several tools are used for tensor decomposition such as rTensor, pyTensor, and MATLAB, since such tools run on a single machine, they are unable to handle large data. Also, while distributed tensor decomposition tools based on Hadoop can handle a scalable tensor, its computing speed is too slow. In this paper, we propose S-PARAFAC, which is a tensor decomposition tool based on Apache Spark, in distributed in-memory environments. We converted the PARAFAC algorithm into an Apache Spark version that enables rapid processing of tensor data. We also compared the performance of the Hadoop based tensor tool and S-PARAFAC. The result showed that S-PARAFAC is approximately 4~25 times faster than the Hadoop based tensor tool.

• International Journal of Contents
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• v.12 no.3
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• pp.22-28
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• 2016

Tensor with missing or incomplete values is a ubiquitous problem in various fields such as biomedical signal processing, image processing, and social network analysis. In this paper, we considered how to reconstruct a dataset with missing values by using tensor form which is called tensor completion process. We applied Tucker factorization to solve tensor completion which was built base on optimization problem. We formulated the optimization objective function using components of Tucker model after decomposing. The weighted least square matric contained only known values of the tensor with low rank in its modes. A first order optimization method, namely Nonlinear Conjugated Gradient, was applied to solve the optimization problem. We demonstrated the effectiveness of the proposed method in EEG signals with about 70% missing entries compared to other algorithms. The relative error was proposed to compare the difference between original tensor and the process output.

• 한국정보디스플레이학회:학술대회논문집
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• 2007.08a
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• pp.517-519
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• 2007

We report our study on the implementation of Q tensor approach into three-dimensional finite element method (FEM) numerical solver. The comparative simulation results demonstrated the possibility of a different director configuration in between Q tensor method and vector method. The comparative study confirmed that Q Tensor implementation is more appropriate for OCB analysis than the vector method.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.603-613
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• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• Journal of Astronomy and Space Sciences
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• v.37 no.2
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• pp.131-142
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• 2020

As the laws of physics are expressed in a manner that makes their invariance under coordinate transformations manifest, they should be written in terms of tensors. Furthermore, tensors make manifest the characteristics and behaviors of electromagnetic fields through inhomogeneous, anisotropic, and compressible media. Electromagnetic fields are expressed completely in tensor form, F^αβ, which implies both electric field ${\overrightarrow{E}}$ and magnetic field ${\overrightarrow{B}}$ rather than separately in the vector fields. This study presents the Mathematica platform that generates and transforms a second-rank antisymmetric field-strength tensor F^αβ and whiskbroom pattern in Minkowski space. The platforms enhance the capabilities of students and researchers in tensor analysis and improves comprehension of the elegant features of complete structure in physics.

• Smart Media Journal
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• v.7 no.4
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• pp.90-98
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• 2018

A Multilinear LDA Method of Tensor Representation for ECG Signal Based Individual Identification Electrocardiogram signals, included in the cardiac electrical activity, are often analyzed and used for various purposes such as heart rate measurement, heartbeat rhythm test, heart abnormality diagnosis, emotion recognition and biometrics. The objective of this paper is to perform individual identification operation based on Multilinear Linear Discriminant Analysis (MLDA) with the tensor feature. The MLDA can solve dimensional aspects of classification problems in high-dimensional tensor, and correlated subspaces can be used to distinguish between different classes. In order to evaluate the performance, we used MPhysionet's MIT-BIH database. The experimental results on this database showed that the individual identification by MLDA outperformed that by PCA and LDA.

• Proceedings of the KIEE Conference
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• 1996.07a
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• pp.169-171
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• 1996

Recently, the finite element analysis(FEM) using two dimensional magnetic permeability tensor was introduced to calculate the magnetic field considering the rotational hysteresis. We obtain the tensor matrix from the measured data using two-dimensional magnetic measuring apparatus. We calculate the induced magnetic flux density and the rotational hysteresis loss under the model with the same condition with the measuring apparatus. Therefore we show that FEM with tensor can be used to calculate the magnetic flux density and the rotational hysteresis loss in the arbitrary rotational magnetic field.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1097-1105
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• 2015

The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of $2_{\otimes}$-auto Engel groups is introduced and we prove that if G is a $2_{\otimes}$-auto Engel group, then $G{\otimes}$ Aut(G) is abelian. Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.

• Convergence Security Journal
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• v.22 no.4
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• pp.129-133
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• 2022

Deep learning frameworks are still evolving, and there are various frameworks. Typical deep learning frameworks include TensorFlow, PyTorch, and Keras. The Deepram framework utilizes optimization models in image classification through image learning. In this paper, we use the TensorFlow and PyTorch frameworks, which are most widely used in the deep learning image recognition field, to proceed with image learning, and compare and analyze the results derived in this process to know the optimized framework. was made.