• Title/Summary/Keyword: Matrix Computation

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Connection between Fourier of Signal Processing and Shannon of 5G SmartPhone (5G 스마트폰의 샤논과 신호처리의 푸리에의 표본화에서 만남)

  • Kim, Jeong-Su;Lee, Moon-Ho
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.17 no.6
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    • pp.69-78
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    • 2017
  • Shannon of the 5G smartphone and Fourier of the signal processing meet in the sampling theorem (2 times the highest frequency 1). In this paper, the initial Shannon Theorem finds the Shannon capacity at the point-to-point, but the 5G shows on the Relay channel that the technology has evolved into Multi Point MIMO. Fourier transforms are signal processing with fixed parameters. We analyzed the performance by proposing a 2N-1 multivariate Fourier-Jacket transform in the multimedia age. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^{\dot{+}}=nl_n$, where $A^{\dot{+}}$ is the transpose matrix of the element-wise inverse of A, that is, $A^{\dot{+}}=(a^{-1}_{kj})$, which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.

Separations and Feature Extractions for Image Signals Using Independent Component Analysis Based on Neural Networks of Efficient Learning Rule (효율적인 학습규칙의 신경망 기반 독립성분분석을 이용한 영상신호의 분리 및 특징추출)

  • Cho, Yong-Hyun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.13 no.2
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    • pp.200-208
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    • 2003
  • This paper proposes a separation and feature extraction of image signals using the independent component analysis(ICA) based on neural networks of efficient learning rule. The proposed learning rule is a hybrid fixed-point(FP) algorithm based on secant method and momentum. Secant method is applied to improve the performance by simplifying the 1st-order derivative computation for optimizing the objective function, which is to minimize the mutual informations of the independent components. The momentum is applied for high-speed convergence by restraining the oscillation in the process of converging to the optimal solution. The proposed algorithm has been applied to the composite images generated by random mixing matrix from the 10 images of $512\times512$-pixel. The simulation results show that the proposed algorithm has better performances of the separation speed and rate than those using the FP algorithm based on Newton and secant method. The proposed algorithm has been also applied to extract the features using a 3 set of 10,000 image patches from the 10 fingerprints of $256\times256$-pixel and the front and the rear paper money of $480\times225$-pixel, respectively, The simulation results show that the proposed algorithm has also better extraction speed than those using the another methods. Especially, the 160 basis vectors(features) of $16\times16$-pixel show the local features which have the characteristics of spatial frequency and oriented edges in the images.

Magnetic Investigation of the Yangsan Fault (양산 단층에 대한 자력탐사 연구)

  • Kwon, Byung-Doo;Lee, Ki-Won
    • Economic and Environmental Geology
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    • v.24 no.4
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    • pp.421-434
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    • 1991
  • Ground magnetic surveys were conducted at four areas where the Yangsan fault, the most prominent lineament in the Kyeongsang basin, appears to be passed through. For data processing, IGRF correction, upward continuation and reduction-to-the-pole were performed. The automatic inversion by using a matrix computation method, which takes the depth to bottom layer of the horizontal two layer structure as the model parameter, has been attempted to delineate the subsurface structure. Upward continuation of the surface magnetic map to the same level of the aeromagnetic survey (KIER, 1989) resulted in very similiar patterns to those of aeromagnetic data. Subsurface modeling of eight profile data show that the strike and dip of the Yangsan fault in study areas are $N6^{\circ}-15^{\circ}E$, and near vertical to somewhat eastward, repectively, despite of the local lithological contrast of each study area. It seems that the magnetic effect of faulting in the study area 1, which locates in the most northern part of the survey areas, is disturbed by that of igneous intrusion. At study area 2, the possibility of volcanic or igneous intrusion, which is 200-300 meters wide along the fault plane was presented. At study area 3, unlike other study areas, distinct fracture zone of 500-700 meters in width was revealed along the surface fault line. The andesitic rocks of the study area 4 have very high susceptibilities and the fault line on surface of this area was shifted about 500 meter eastward, as compared with the inferred fault line by the previous study.

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A Comprehensive Groundwater Modeling using Multicomponent Multiphase Theory: 1. Development of a Multidimensional Finite Element Model (다중 다상이론을 이용한 통합적 지하수 모델링: 1. 다차원 유한요소 모형의 개발)

  • Joon Hyun Kim
    • Journal of Korea Soil Environment Society
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    • v.1 no.1
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    • pp.89-102
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    • 1996
  • An integrated model is presented to describe underground flow and mass transport, using a multicomponent multiphase approach. The comprehensive governing equation is derived considering mass and force balances of chemical species over four phases(water, oil, air, and soil) in a schematic elementary volume. Compact and systemati notations of relevant variables and equations are introduced to facilitate the inclusion of complex migration and transformation processes, and variable spatial dimensions. The resulting nonlinear system is solved by a multidimensional finite element code. The developed code with dynamic array allocation, is sufficiently flexible to work across a wide spectrum of computers, including an IBM ES 9000/900 vector facility, SP2 cluster machine, Unix workstations and PCs, for one-, two and three-dimensional problems. To reduce the computation time and storage requirements, the system equations are decoupled and solved using a banded global matrix solver, with the vector and parallel processing on the IBM 9000. To avoide the numerical oscillations of the nonlinear problems in the case of convective dominant transport, the techniques of upstream weighting, mass lumping, and elementary-wise parameter evaluation are applied. The instability and convergence criteria of the nonlinear problems are studied for the one-dimensional analogue of FEM and FDM. Modeling capacity is presented in the simulation of three dimensional composite multiphase TCE migration. Comprehesive simulation feature of the code is presented in a companion paper of this issue for the specific groundwater or flow and contamination problems.

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Correction for SPECT image distortion by non-circular detection orbits (비원형 궤도에서의 검출에 의한 SPECT 영상 왜곡 보정)

  • Lee, Nam-Yong
    • Journal of the Institute of Convergence Signal Processing
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    • v.8 no.3
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    • pp.156-162
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    • 2007
  • The parallel beam SPECT system acquires projection data by using collimators in conjunction with photon detectors. The projection data of the parallel beam SPECT system is, however, blurred by the point response function of the collimator that is used to define the range of directions where photons can be detected. By increasing the number of parallel holes per unit area in collimator, one can reduce such blurring effect. This approach also, however, has the blurring problem if the distance between the object and the collimator becomes large. In this paper we consider correction methods for artifacts caused by non-circular orbit of parallel beam SPECT with many parallel holes per detector cell. To do so, we model the relationship between the object and its projection data as a linear system, and propose an iterative reconstruction method including artifacts correction. We compute the projector and the backprojector, which are required in iterative method, as a sum of convolutions with distance-dependent point response functions instead of matrix form, where those functions are analytically computed from a single function. By doing so, we dramatically reduce the computation time and memory required for the generation of the projector and the backprojector. We conducted several simulation studies to compare the performance of the proposed method with that of conventional Fourier method. The result shows that the proposed method outperforms Fourier methods objectively and subjectively.

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An Efficient Composite Image Separation by Using Independent Component Analysis Based on Neural Networks (신경망 기반 독립성분분석을 이용한 효율적인 복합영상분리)

  • Cho, Yong-Hyun;Park, Yong-Soo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.12 no.3
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    • pp.210-218
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    • 2002
  • This paper proposes an efficient separation method of the composite images by using independent component analysis(ICA) based on neural networks of the approximate learning algorithm. The Proposed learning algorithm is the fixed point(FP) algorithm based on Secant method which can be approximately computed by only the values of function for estimating the root of objective function for optimizing entropy. The secant method is an alternative of the Newton method which is essential to differentiate the function for estimating the root. It can achieve a superior property of the FP algorithm for ICA due to simplify the composite computation of differential process. The proposed algorithm has been applied to the composite signals and image generated by random mixing matrix in the 4 signal of 500-sample and the 10 images of $512{\times}512-pixel$, respectively The simulation results show that the proposed algorithm has better performance of the learning speed and the separation than those using the conventional algorithm based method. It also solved the training performances depending on initial points setting and the nonrealistic learning time for separating the large size image by using the conventional algorithm.

Recommender Systems using Structural Hole and Collaborative Filtering (구조적 공백과 협업필터링을 이용한 추천시스템)

  • Kim, Mingun;Kim, Kyoung-Jae
    • Journal of Intelligence and Information Systems
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    • v.20 no.4
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    • pp.107-120
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    • 2014
  • This study proposes a novel recommender system using the structural hole analysis to reflect qualitative and emotional information in recommendation process. Although collaborative filtering (CF) is known as the most popular recommendation algorithm, it has some limitations including scalability and sparsity problems. The scalability problem arises when the volume of users and items become quite large. It means that CF cannot scale up due to large computation time for finding neighbors from the user-item matrix as the number of users and items increases in real-world e-commerce sites. Sparsity is a common problem of most recommender systems due to the fact that users generally evaluate only a small portion of the whole items. In addition, the cold-start problem is the special case of the sparsity problem when users or items newly added to the system with no ratings at all. When the user's preference evaluation data is sparse, two users or items are unlikely to have common ratings, and finally, CF will predict ratings using a very limited number of similar users. Moreover, it may produces biased recommendations because similarity weights may be estimated using only a small portion of rating data. In this study, we suggest a novel limitation of the conventional CF. The limitation is that CF does not consider qualitative and emotional information about users in the recommendation process because it only utilizes user's preference scores of the user-item matrix. To address this novel limitation, this study proposes cluster-indexing CF model with the structural hole analysis for recommendations. In general, the structural hole means a location which connects two separate actors without any redundant connections in the network. The actor who occupies the structural hole can easily access to non-redundant, various and fresh information. Therefore, the actor who occupies the structural hole may be a important person in the focal network and he or she may be the representative person in the focal subgroup in the network. Thus, his or her characteristics may represent the general characteristics of the users in the focal subgroup. In this sense, we can distinguish friends and strangers of the focal user utilizing the structural hole analysis. This study uses the structural hole analysis to select structural holes in subgroups as an initial seeds for a cluster analysis. First, we gather data about users' preference ratings for items and their social network information. For gathering research data, we develop a data collection system. Then, we perform structural hole analysis and find structural holes of social network. Next, we use these structural holes as cluster centroids for the clustering algorithm. Finally, this study makes recommendations using CF within user's cluster, and compare the recommendation performances of comparative models. For implementing experiments of the proposed model, we composite the experimental results from two experiments. The first experiment is the structural hole analysis. For the first one, this study employs a software package for the analysis of social network data - UCINET version 6. The second one is for performing modified clustering, and CF using the result of the cluster analysis. We develop an experimental system using VBA (Visual Basic for Application) of Microsoft Excel 2007 for the second one. This study designs to analyzing clustering based on a novel similarity measure - Pearson correlation between user preference rating vectors for the modified clustering experiment. In addition, this study uses 'all-but-one' approach for the CF experiment. In order to validate the effectiveness of our proposed model, we apply three comparative types of CF models to the same dataset. The experimental results show that the proposed model outperforms the other comparative models. In especial, the proposed model significantly performs better than two comparative modes with the cluster analysis from the statistical significance test. However, the difference between the proposed model and the naive model does not have statistical significance.