• Journal of the Korea Society of Computer and Information
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• v.20 no.12
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• pp.67-74
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• 2015

The heat conduction equation, a type of a Poisson equation which can be applied in various areas of engineering is calculating its value with the iteration method in general. The equation which had difference discretization of the heat conduction equation is the simultaneous equation, and each line has the characteristic of expressing in sparse matrix of the equivalent number of none-zero elements with neighboring grids. In this paper, we propose a data structure for sparse matrix that can calculate the value faster with less memory use calculate the heat conduction equation. To verify whether the proposed data structure efficiently calculates the value compared to the other sparse matrix representations, we apply the representative iteration method, CG (Conjugate Gradient), and presents experiment results of time consumed to get values, calculation time of each step and relevant time consumption ratio, and memory usage amount. The results of this experiment could be used to estimate main elements of calculating the value of the general heat conduction equation, such as time consumed, the memory usage amount.

• Communications for Statistical Applications and Methods
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• v.29 no.6
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• pp.655-664
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• 2022

On the motivation by an integrative study of multi-omics data, we are interested in estimating the structure of the sparse cross correlation matrix of two high-dimensional random vectors. We rewrite the problem as a multiple testing problem and propose a new method to estimate the sparse structure of the cross correlation matrix. To do so, we test the correlation coefficients simultaneously and threshold the correlation coefficients by controlling FRD at a predetermined level α. Further, we apply the proposed method and an alternative adaptive thresholding procedure by Cai and Liu (2016) to the integrative analysis of the protein expression data (X) and the mRNA expression data (Y) in TCGA breast cancer cohort. By varying the FDR level α, we show that the new procedure is consistently more efficient in estimating the sparse structure of cross correlation matrix than the alternative one.

• Journal of Korea Spatial Information System Society
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• v.12 no.1
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• pp.49-56
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• 2010

Many researches of frequent pattern mining technique for detecting unknown patterns on spatial data have studied actively. Existing data structures have classified into tree-structure and array-structure, and those structures show the weakness of performance on dense or sparse data. Since spatial data have obtained the characteristics of dense and sparse patterns, it is important for us to mine quickly dense and sparse patterns using only single algorithm. In this paper, we propose novel data structure as compressed patricia frequent pattern tree and frequent pattern mining algorithm based on proposed data structure which can detect frequent patterns quickly in terms of both dense and sparse frequent patterns mining. In our experimental result, proposed algorithm proves about 10 times faster than existing FP-Growth algorithm on both dense and sparse data.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.9
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• pp.3211-3230
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• 2014

Recently, sparse coding has achieved remarkable success in image representation tasks. In practice, the performance of clustering can be significantly improved if limited label information is incorporated into sparse coding. To this end, in this paper, a novel semi-supervised algorithm, called constrained sparse concept coding (CSCC), is proposed for image representation. CSCC considers limited label information into graph embedding as additional hard constraints, and hence obtains embedding results that are consistent with label information and manifold structure information of the original data. Therefore, CSCC can provide a sparse representation which explicitly utilizes the prior knowledge of the data to improve the discriminative power in clustering. Besides, a kernelized version of our proposed CSCC, namely kernel constrained sparse concept coding (KCSCC), is developed to deal with nonlinear data, which leads to more effective clustering performance. The experimental evaluations on the MNIST, PIE and Yale image sets show the effectiveness of our proposed algorithms.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.7
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• pp.3594-3607
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• 2017

The traditional feature extraction methods such as principal component analysis (PCA) cannot obtain the local structure of the samples, and locally linear embedding (LLE) cannot obtain the global structure of the samples. However, a common drawback of existing PCA and LLE algorithm is that they cannot deal well with the sparse problem of the samples. Therefore, by integrating the globality of PCA and the locality of LLE with a sparse constraint, we developed an improved and unsupervised difference algorithm called Sparse Difference Embedding (SDE), for dimensionality reduction of high-dimensional data in small sample size problems. Significantly differing from the existing PCA and LLE algorithms, SDE seeks to find a set of perfect projections that can not only impact the locality of intraclass and maximize the globality of interclass, but can also simultaneously use the Lasso regression to obtain a sparse transformation matrix. This characteristic makes SDE more intuitive and more powerful than PCA and LLE. At last, the proposed algorithm was estimated through experiments using the Yale and AR face image databases and the USPS handwriting digital databases. The experimental results show that SDE outperforms PCA LLE and UDP attributed to its sparse discriminating characteristics, which also indicates that the SDE is an effective method for face recognition.

• Smart Structures and Systems
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• v.25 no.2
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• pp.123-133
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• 2020

Compressive sensing (CS) is a newly developed data acquisition and processing technique that takes advantage of the sparse structure in signals. Normally signals in their primitive space or format are reconstructed from their compressed measurements for further treatments, such as modal analysis for vibration data. This approach causes problems such as leakage, loss of fidelity, etc., and the computation of reconstruction itself is costly as well. Therefore, it is appealing to directly work on the compressed data without prior reconstruction of the original data. In this paper, a direct approach for modal analysis of damped systems is proposed by decomposing the compressed measurements with an appropriate dictionary. The damped free vibration function is adopted to form atoms in the dictionary for the following sparse decomposition. Compared with the normally used Fourier bases, the damped free vibration function spans a space with both the frequency and damping as the control variables. In order to efficiently search the enormous two-dimension dictionary with frequency and damping as variables, a two-step strategy is implemented combined with the Orthogonal Matching Pursuit (OMP) to determine the optimal atom in the dictionary, which greatly reduces the computation of the sparse decomposition. The performance of the proposed method is demonstrated by a numerical and an experimental example, and advantages of the method are revealed by comparison with another such kind method using POD technique.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1215-1232
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• 2015

In the present paper, a method for identifying damage in a multi storeyed shear building structure is presented using minimum number of modal parameters of the structure. A damage at any level of the structure may lead to a major failure if the damage is not attended at appropriate time. Hence an early detection of damage is essential. The proposed identification methodology requires experimentally determined sparse modal data of any particular mode as input to detect the location and extent of damage in the structure. Here, the first natural frequency and corresponding partial mode shape values are used as input to the model and results are compared by changing the sensor placement locations at different floors to conclude the best location of sensors for accurate damage identification. Initially experimental data are simulated numerically by solving eigen value problem of the damaged structure with inclusion of random noise on the vibration characteristics. Reliability of the procedure has been demonstrated through a few examples of multi storeyed shear structure with different damage scenarios and various noise levels. Validation of the methodology has also been done using dynamic data obtained through experiment conducted on a laboratory scale steel structure.

• Smart Structures and Systems
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• v.21 no.1
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• pp.1-14
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• 2018

A method is proposed to detect structural damages in the presence of damping using noisy data. This method uses Frequency Response Function (FRF) and Mode-Shapes as the input parameters for a system of Couple Sparse Coding (CSC) to study the healthy state of the structure. To obtain appropriate patterns of FRF for CSC training, Principal Component Analysis (PCA) technique is adopted to reduce the full-size FRF to overcome over-fitting and convergence problems in machine-learning training. To verify the proposed method, a numerical two-story frame structure is employed. A system of individual CSCs is trained with FRFs and mode-shapes, and then termed ensemble to detect the health condition of the structure. The results demonstrate that the proposed method is accurate in damage identification even in presence of up to 20% noisy data and 5% unconsidered damping ratio. Furthermore, it can be concluded that CSC ensemble is highly efficient to detect the location and the severity of damages in comparison to the individual CSC trained only with FRF data.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.6
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• pp.2634-2648
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• 2020

In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.657-667
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• 2019

This paper studies synthetic aperture radar (SAR) imaging problem which the scatterers are often distributed in block sparse pattern. To exploiting the sparse geometrical feature, a Kronecker constrained SAR imaging algorithm is proposed by combining the block sparse characteristics with the multiway sparse reconstruction framework with Tucker modeling. We validate the proposed algorithm via real data and it shows that the our algorithm can achieve better accuracy and convergence than the reference methods even in the demanding environment. Meanwhile, the complexity is smaller than that of the existing methods. The simulation experiments confirmed the effectiveness of the algorithm as well.