• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.1-29
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• 2007

Suppose one is trying to estimate a high dimensional vector of parameters from a series of one observation per parameter. Often, it is possible to take advantage of sparsity in the parameters by thresholding the data in an appropriate way. A marginal maximum likelihood approach, within a suitable Bayesian structure, has excellent properties. For very sparse signals, the procedure chooses a large threshold and takes advantage of the sparsity, while for signals where there are many non-zero values, the method does not perform excessive smoothing. The scope of the method is reviewed and demonstrated, and various theoretical, practical and computational issues are discussed, in particularly exploring the wide potential and applicability of the general approach, and the way it can be used within more complex thresholding problems such as curve estimation using wavelets.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4556-4572
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• 2015

Dynamic texture (DT) recognition is a challenging problem in numerous applications. In this study, we propose a new algorithm for DT recognition based on group sparsity structure in conjunction with chaotic feature vector. Bag-of-words model is used to represent each video as a histogram of the chaotic feature vector, which is proposed to capture self-similarity property of the pixel intensity series. The recognition problem is then cast to a group sparsity model, which can be efficiently optimized through alternating direction method of multiplier algorithm. Experimental results show that the proposed method exhibited the best performance among several well-known DT modeling techniques.

• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1090-1096
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• 2001

In this paper, new methods for efficiently solving linear acceleration equations of multibody dynamic simulation exploiting sparsity for real-time simulation are presented. The coefficient matrix of the equations tends to have a large number of zero entries according to the relative joint coordinate numbering. By adequate joint coordinate numbering, the matrix has minimum off-diagonal terms and a block pattern of non-zero entries and can be solved efficiently. The proposed methods, using sparse Cholesky method and recursive block mass matrix method, take advantages of both the special structure and the sparsity of the coefficient matrix to reduce computation time. The first method solves the η$\times$η sparse coefficient matrix for the accelerations, where η denotes the number of relative coordinates. In the second method, for vehicle dynamic simulation, simple manipulations bring the original problem of dimension η$\times$η to an equivalent problem of dimension 6$\times$6 to be solved for the accelerations of a vehicle chassis. For vehicle dynamic simulation, the proposed solution methods are proved to be more efficient than the classical approaches using reduced Lagrangian multiplier method. With the methods computation time for real-time vehicle dynamic simulation can be reduced up to 14 per cent compared to the classical approach.

• Journal of Information Processing Systems
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• v.15 no.2
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• pp.410-421
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• 2019

Distributed compressed sensing (DCS) states that we can recover the sparse signals from very few linear measurements. Various studies about DCS have been carried out recently. In many practical applications, there is no prior information except for standard sparsity on signals. The typical example is the sparse signals have block-sparse structures whose non-zero coefficients occurring in clusters, while the cluster pattern is usually unavailable as the prior information. To discuss this issue, a new algorithm, called backtracking-based adaptive orthogonal matching pursuit for block distributed compressed sensing (DCSBBAOMP), is proposed. In contrast to existing block methods which consider the single-channel signal reconstruction, the DCSBBAOMP resorts to the multi-channel signals reconstruction. Moreover, this algorithm is an iterative approach, which consists of forward selection and backward removal stages in each iteration. An advantage of this method is that perfect reconstruction performance can be achieved without prior information on the block-sparsity structure. Numerical experiments are provided to illustrate the desirable performance of the proposed method.

• Genomics & Informatics
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• v.20 no.4
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• pp.48.1-48.7
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• 2022

Penalized regression has been widely used in genome-wide association studies for joint analyses to find genetic associations. Among penalized regression models, the least absolute shrinkage and selection operator (Lasso) method effectively removes some coefficients from the model by shrinking them to zero. To handle group structures, such as genes and pathways, several modified Lasso penalties have been proposed, including group Lasso and sparse group Lasso. Group Lasso ensures sparsity at the level of pre-defined groups, eliminating unimportant groups. Sparse group Lasso performs group selection as in group Lasso, but also performs individual selection as in Lasso. While these sparse methods are useful in high-dimensional genetic studies, interpreting the results with many groups and coefficients is not straightforward. Lasso's results are often expressed as trace plots of regression coefficients. However, few studies have explored the systematic visualization of group information. In this study, we propose a multi-level polar Lasso (MP-Lasso) chart, which can effectively represent the results from group Lasso and sparse group Lasso analyses. An R package to draw MP-Lasso charts was developed. Through a real-world genetic data application, we demonstrated that our MP-Lasso chart package effectively visualizes the results of Lasso, group Lasso, and sparse group Lasso.

• Journal of the military operations research society of Korea
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• v.29 no.1
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• pp.28-42
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• 2003

The simplex method requires basis update in each iteration, which is the most time consuming process. Several methods have been developed for the update of basis which is represented in LU factorized form, such as Bartels-Golub's method, Forrest-Tomlin's method, Reid's method, Saunders's method, etc. In this research, we compare between the updating methods in terms of sparsity, data structure and computing time issues. The analysis is mainly based on the computational experience.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.63-66
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• 1998

In the implementation of the simplex method program, the representation and the maintenance of basis matrix is very important, In the experimental study, we investigates Suhl's idea in the LU factorization and LU update of basis matrix. First, the triangularization of basis matrix is implemented and its efficiency is shown. Second, various technique in the dynamic Markowitz's ordering and threshold pivoting are presented. Third, modified Forrest-Tomlin LU update method exploiting sparsity is presented. Fourth, as a storage scheme of LU factors, Gustavson data structure is explained. Fifth, efficient timing of reinversion is developed. Finally, we show that modified Forrest-Tomlin method with Gustavson data structure is superior more than 30% to the Reid method with linked list data structure.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.2
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• pp.205-211
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• 2012

The retrieved documents have to be transformed into proper data structure for the clustering algorithms of statistics and machine learning. A popular data structure for document clustering is document-term matrix. This matrix has the occurred frequency value of a term in each document. There is a sparsity problem in this matrix because most frequencies of the matrix are 0 values. This problem affects the clustering performance. The sparseness of document-term matrix decreases the performance of clustering result. So, this research uses the factor score by factor analysis to solve the sparsity problem in document clustering. The document-term matrix is transformed to document-factor score matrix using factor scores in this paper. Also, the document-factor score matrix is used as input data for document clustering. To compare the clustering performances between document-term matrix and document-factor score matrix, this research applies two typed matrices to self organizing map (SOM) clustering.

• Korean Management Science Review
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• v.15 no.1
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• pp.49-62
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• 1998

The purpose of this paper is to develope a large-scale simplex method program LPAKO. Various up-to-date techniques are argued and implemented. In LPAKO, basis matrices are stored in a LU factorized form, and Reid's method is used to update LU maintaining high sparsity and numerical stability, and further Markowitz's ordering is used in factorizing a basis matrix into a sparse LU form. As the data structures of basis matrix, Gustavson's data structure and row-column linked list structure are considered. The various criteria for reinversion are also discussed. The dynamic steepest-edge simplex algorithm is used for selection of an entering variable, and a new variation of the MINOS' perturbation technique is suggested for the resolution of degeneracy. Many preprocessing and scaling techniques are implemented. In addition, a new, effective initial basis construction method are suggested, and the criteria for optimality and infeasibility are suggested respectively. Finally, LPAKO is compared with MINOS by test results.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.275-280
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• 2005

The principal context of this research is the approach to an artificial neural network algorithm which solves multivariable nonlinear equation systems by estimating the state of line power flow. First a dynamical neural network with feedback is used to find the minimum value of the objective function at each iteration of the state estimator algorithm. In second step a two-layer neural network structures is derived to implement all of the different matrix-vector products that arise in neural network state estimator analysis. For hardware requirements, as they relate to the total number of internal connections, the architecture developed here preserves in its structure the pronounced sparsity of power networks for which state the estimator analysis is to be carried out. A principal feature of the architecture is that the computing time overheads in solution are independent of the dimensions or structure of the equation system. It is here where the ultrahigh-speed of massively parallel computing in neural networks can offer major practical benefit.