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1 – 10 of over 2000Yuanqing Li and Andrzej Cichocki
Proposes a non‐negative matrix factorization method.
Abstract
Purpose
Proposes a non‐negative matrix factorization method.
Design/methodology approach
Presents an algorithm for finding a suboptimal basis matrix. This is controlled by data cluster centers which can guarantee that the coefficient is very sparse. This leads to the proposition of an application of non‐matrix factorization for blind sparse source separation with less sensors than sources.
Findings
Two simulation examples reveal the validity and performance of the algorithm in this paper.
Originality/value
Using the approach in this paper, the sparse sources can be recovered even if the sources are overlapped to some degree.
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Keywords
Maryam Daei and S. Hamid Mirmohammadi
The efficiency of the finite element analysis via force method depends on the overall flexibility matrix of the structure, while this matrix is directly affected from null bases…
Abstract
Purpose
The efficiency of the finite element analysis via force method depends on the overall flexibility matrix of the structure, while this matrix is directly affected from null bases vectors. As the null bases for an indeterminate structure are not unique, for an optimal analysis, the selected null bases should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrix. This paper aims to present an efficient method for the formation of optimal flexibility matrix of finite element models comprising tetrahedron elements via mathematical optimization technique.
Design/methodology/approach
For this purpose, a linear mixed integer programming model is presented for finding sparse solution of underdetermined linear system, which is correspond to sparse null vector. The charged system search algorithm is improved and used to find the best generator for formation of null bases.
Findings
The efficiency of the present method is illustrated through some examples. The proposed method leads to highly sparse, banded and accurate null basis matrices. It makes an efficient force method feasible for the analysis of finite element model comprising tetrahedron elements.
Originality/value
The force method, in which the member forces are used as unknowns, can be appealing to engineers. The main problem in the application of the force method is the formation of a self-stress matrix corresponding to a sparse flexibility matrix. In this paper, the highly sparse, banded and accurate null basis matrices gains by using mathematical optimization technique.
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Junying Chen, Zhanshe Guo, Fuqiang Zhou, Jiangwen Wan and Donghao Wang
As the limited energy of wireless sensor networks (WSNs), energy-efficient data-gathering algorithms are required. This paper proposes a compressive data-gathering algorithm based…
Abstract
Purpose
As the limited energy of wireless sensor networks (WSNs), energy-efficient data-gathering algorithms are required. This paper proposes a compressive data-gathering algorithm based on double sparse structure dictionary learning (DSSDL). The purpose of this paper is to reduce the energy consumption of WSNs.
Design/methodology/approach
The historical data is used to construct a sparse representation base. In the dictionary-learning stage, the sparse representation matrix is decomposed into the product of double sparse matrices. Then, in the update stage of the dictionary, the sparse representation matrix is orthogonalized and unitized. The finally obtained double sparse structure dictionary is applied to the compressive data gathering in WSNs.
Findings
The dictionary obtained by the proposed algorithm has better sparse representation ability. The experimental results show that, the sparse representation error can be reduced by at least 3.6% compared with other dictionaries. In addition, the better sparse representation ability makes the WSNs achieve less measurement times under the same accuracy of data gathering, which means more energy saving. According to the results of simulation, the proposed algorithm can reduce the energy consumption by at least 2.7% compared with other compressive data-gathering methods under the same data-gathering accuracy.
Originality/value
In this paper, the double sparse structure dictionary is introduced into the compressive data-gathering algorithm in WSNs. The experimental results indicate that the proposed algorithm has good performance on energy consumption and sparse representation.
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Keywords
Christos K. Filelis-Papadopoulos and George A. Gravvanis
Large sparse least-squares problems arise in different scientific disciplines such as optimization, data analysis, machine learning and simulation. This paper aims to propose a…
Abstract
Purpose
Large sparse least-squares problems arise in different scientific disciplines such as optimization, data analysis, machine learning and simulation. This paper aims to propose a two-level hybrid direct-iterative scheme, based on novel block independent column reordering, for efficiently solving large sparse least-squares linear systems.
Design/methodology/approach
Herewith, a novel block column independent set reordering scheme is used to separate the columns in two groups: columns that are block independent and columns that are coupled. The permutation scheme leads to a two-level hierarchy. Using this two-level hierarchy, the solution of the least-squares linear system results in the solution of a reduced size Schur complement-type square linear system, using the preconditioned conjugate gradient (PCG) method as well as backward substitution using the upper triangular factor, computed through sparse Q-less QR factorization of the columns that are block independent. To improve the convergence behavior of the PCG method, the upper triangular factor, computed through sparse Q-less QR factorization of the coupled columns, is used as a preconditioner. Moreover, to further reduce the fill-in, then the column approximate minimum degree (COLAMD) algorithm is used to permute the block consisting of the coupled columns.
Findings
The memory requirements for solving large sparse least-squares linear systems are significantly reduced compared to Q-less QR decomposition of the original as well as the permuted problem with COLAMD. The memory requirements are reduced further by choosing to form larger blocks of independent columns. The convergence behavior of the iterative scheme is improved due to the chosen preconditioning scheme. The proposed scheme is inherently parallel due to the introduction of block independent column reordering.
Originality/value
The proposed scheme is a hybrid direct-iterative approach for solving sparse least squares linear systems based on the implicit computation of a two-level approximate pseudo-inverse matrix. Numerical results indicating the applicability and effectiveness of the proposed scheme are given.
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Keywords
Zhen Ma, Degan Zhang, Si Liu, Jinjie Song and Yuexian Hou
The performance of the measurement matrix directly affects the quality of reconstruction of compressive sensing signal, and it is also the key to solve practical problems. In…
Abstract
Purpose
The performance of the measurement matrix directly affects the quality of reconstruction of compressive sensing signal, and it is also the key to solve practical problems. In order to solve data collection problem of wireless sensor network (WSN), the authors design a kind of optimization of sparse matrix. The paper aims to discuss these issues.
Design/methodology/approach
Based on the sparse random matrix, it optimizes the seed vector, which regards elements in the diagonal matrix of Hadamard matrix after passing singular value decomposition (SVD). Compared with the Toeplitz matrix, it requires less number of independent random variables and the matrix information is more concentrated.
Findings
The performance of reconstruction is better than that of Gaussian random matrix. The authors also apply this matrix to the data collection scheme in WSN. The result shows that it costs less energy and reduces the collection frequency of nodes compared with general method.
Originality/value
The authors design a kind of optimization of sparse matrix. Based on the sparse random matrix, it optimizes the seed vector, which regards elements in the diagonal matrix of Hadamard matrix after passing SVD. Compared with the Toeplitz matrix, it requires less number of independent random variables and the matrix information is more concentrated.
Details
Keywords
In the present study we introduce a new recursive matrix inversion (RMI) algorithm for a distributed memory computer. The RMI algorithm was designed to meet the requirements of…
Abstract
In the present study we introduce a new recursive matrix inversion (RMI) algorithm for a distributed memory computer. The RMI algorithm was designed to meet the requirements of high performance flexible software for implementing different parallel optimization algorithms. Special consideration has been taken to ensure the usability and portability of the algorithm. The results we present show that a significant improvement in performance is attainable over the LU‐factorization algorithm included in the LAPACK library.
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Farzad Shafiei Dizaji and Mehrdad Shafiei Dizaji
The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one…
Abstract
Purpose
The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one of the sources of errors. In numerical analysis, sometimes handling numerical errors is challenging. However, by applying appropriate algorithms, these errors are manageable and can be reduced. In this study, five novel topological algorithms were proposed in setting up a structural flexibility matrix, and five different examples were used in applying the proposed algorithms. In doing so round-off errors were reduced remarkably.
Design/methodology/approach
Five new algorithms were proposed in order to optimize the conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.
Findings
(1) Five new algorithms were proposed in order to optimize the conditioning of structural flexibility matrices. (2) A JAVA programming language was written for all five algorithms and a friendly GUI software tool is developed to visualize sub-optimal cycle bases. (3) Topological and algebraic features of the structures were utilized in this study.
Research limitations/implications
This is a multi-objective optimization problem which means that sparsity and well conditioning of a matrix cannot be optimized simultaneously. In conclusion, well-conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.
Practical implications
Engineers always finding mathematical modeling of real-world problems and make them as simple as possible. In doing so, lots of errors will be created and these errors could cause the mathematical models useless. Applying decent algorithms could make the mathematical model as precise as possible.
Social implications
Errors in numerical simulations should reduce due to the fact that they are toxic for real-world applications and problems.
Originality/value
This is an original research. This paper proposes five novel topological mathematical algorithms in order to optimize the structural flexibility matrix.
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R. Kelley Pace and James P. LeSage
We show how to quickly estimate spatial probit models for large data sets using maximum likelihood. Like Beron and Vijverberg (2004), we use the GHK (Geweke-Hajivassiliou-Keane…
Abstract
We show how to quickly estimate spatial probit models for large data sets using maximum likelihood. Like Beron and Vijverberg (2004), we use the GHK (Geweke-Hajivassiliou-Keane) algorithm to perform maximum simulated likelihood estimation. However, using the GHK for large sample sizes has been viewed as extremely difficult (Wang, Iglesias, & Wooldridge, 2013). Nonetheless, for sparse covariance and precision matrices often encountered in spatial settings, the GHK can be applied to very large sample sizes as its operation counts and memory requirements increase almost linearly with n when using sparse matrix techniques.
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R.S. Chen, L. Mo and Edward K.N. Yung
Aims to apply the generalized minimal residual (GMRES) algorithm combined with the fast Fourier transform (FFT) technique to solve dense matrix equations from the mixed potential…
Abstract
Purpose
Aims to apply the generalized minimal residual (GMRES) algorithm combined with the fast Fourier transform (FFT) technique to solve dense matrix equations from the mixed potential integral equation (MPIE) when the planar microstrip circuits are analyzed.
Design/methodology/approach
To enhance the computational efficiency of the GMRES‐FFT algorithm, the multifrontal method is first employed to precondition the matrix equations since their condition numbers can be improved.
Findings
The numerical calculations show that the proposed preconditioned GMRES‐FFT algorithm can converge nearly 30 times faster than the conventional one for the analysis of microstrip circuits. Some typical microstrip discontinuities are analyzed and the good results demonstrate the validity of the proposed algorithm.
Originality/value
In the future, some more efficient preconditioning techniques will be found for the mixed potential integral equation (MPIE) when the planar microstrip circuits are analyzed.
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Keywords
Chemmalar Selvi G. and Lakshmi Priya G.G.
In today’s world, the recommender systems are very valuable systems for the online users, as the World Wide Web is loaded with plenty of available information causing the online…
Abstract
Purpose
In today’s world, the recommender systems are very valuable systems for the online users, as the World Wide Web is loaded with plenty of available information causing the online users to spend more time and money. The recommender systems suggest some possible and relevant recommendation to the online users by applying the recommendation filtering techniques to the available source of information. The recommendation filtering techniques take the input data denoted as the matrix representation which is generally very sparse and high dimensional data in nature. Hence, the sparse data matrix is completed by filling the unknown or missing entries by using many matrix completion techniques. One of the most popular techniques used is the matrix factorization (MF) which aims to decompose the sparse data matrix into two new and small dimensional data matrix and whose dot product completes the matrix by filling the logical values. However, the MF technique failed to retain the loss of original information when it tried to decompose the matrix, and the error rate is relatively high which clearly shows the loss of such valuable information.
Design/methodology/approach
To alleviate the problem of data loss and data sparsity, the new algorithm from formal concept analysis (FCA), a mathematical model, is proposed for matrix completion which aims at filling the unknown or missing entries without loss of valuable information to a greater extent. The proposed matrix completion algorithm uses the clustering technique where the users who have commonly rated the items and have not commonly rated the items are captured into two classes. The matrix completion algorithm fills the mean cluster value of the unknown entries which well completes the matrix without actually decomposing the matrix.
Findings
The experiment was conducted on the available public data set, MovieLens, whose result shows the prediction error rate is minimal, and the comparison with the existing algorithms is also studied. Thus, the application of FCA in recommender systems proves minimum or no data loss and improvement in the prediction accuracy of rating score.
Social implications
The proposed matrix completion algorithm using FCA performs good recommendation which will be more useful for today’s online users in making decision with regard to the online purchasing of products.
Originality/value
This paper presents the new technique of matrix completion adopting the vital properties from FCA which is applied in the recommender systems. Hence, the proposed algorithm performs well when compared to other existing algorithms in terms of prediction accuracy.
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