Journal articles: 'Singular-Value Decomposition (SVD)'

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KOH, MIN-SUNG. "A QUINTET SINGULAR VALUE DECOMPOSITION THROUGH EMPIRICAL MODE DECOMPOSITIONS." Advances in Adaptive Data Analysis 06, no. 02n03 (April 2014): 1450010. http://dx.doi.org/10.1142/s1793536914500101.

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A particular quintet singular valued decomposition (Quintet-SVD) is introduced in this paper via empirical mode decompositions (EMDs). The Quintet-SVD results in four specific orthogonal matrices with a diagonal matrix of singular values. Furthermore, this paper shows relationships between the Quintet-SVD and traditional SVD, generalized low rank approximations of matrices (GLRAM) of one single matrix, and EMDs. One application of the Quintet-SVD for speech enhancement is shown and compared with an application of traditional SVD.

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Lem, Kong Hoong. "Truncated singular value decomposition in ripped photo recovery." ITM Web of Conferences 36 (2021): 04008. http://dx.doi.org/10.1051/itmconf/20213604008.

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Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application of SVD in recovering ripped photos was exploited. Recovery was done by applying truncated SVD iteratively. Performance was evaluated using the Frobenius norm. Results from a few experimental photos were decent.

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Caltenco, J. H., José Luis Lopez-Bonilla, B. E. Carvajal-Gámez, and P. Lam-Estrada. "Singular Value Decomposition." Bulletin of Society for Mathematical Services and Standards 11 (September 2014): 13–20. http://dx.doi.org/10.18052/www.scipress.com/bsmass.11.13.

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We study the SVD of an arbitrary matrix Anxm, especially its subspaces of activation, which leads in natural manner to pseudoinverse of Moore-Bjenhammar-Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution, and our approach gives the Lanczos classification for these systems.

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Liu, Bowen, Balázs Pejó, and Qiang Tang. "Privacy-Preserving Federated Singular Value Decomposition." Applied Sciences 13, no. 13 (June 21, 2023): 7373. http://dx.doi.org/10.3390/app13137373.

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Singular value decomposition (SVD) is a fundamental technique widely used in various applications, such as recommendation systems and principal component analyses. In recent years, the need for privacy-preserving computations has been increasing constantly, which concerns SVD as well. Federated SVD has emerged as a promising approach that enables collaborative SVD computation without sharing raw data. However, existing federated approaches still need improvements regarding privacy guarantees and utility preservation. This paper moves a step further towards these directions: we propose two enhanced federated SVD schemes focusing on utility and privacy, respectively. Using a recommendation system use-case with real-world data, we demonstrate that our schemes outperform the state-of-the-art federated SVD solution. Our utility-enhanced scheme (utilizing secure aggregation) improves the final utility and the convergence speed by more than 2.5 times compared with the existing state-of-the-art approach. In contrast, our privacy-enhancing scheme (utilizing differential privacy) provides more robust privacy protection while improving the same aspect by more than 25%.

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GYONGYOSI, LASZLO, and SANDOR IMRE. "QUANTUM SINGULAR VALUE DECOMPOSITION BASED APPROXIMATION ALGORITHM." Journal of Circuits, Systems and Computers 19, no. 06 (October 2010): 1141–62. http://dx.doi.org/10.1142/s0218126610006797.

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Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. The proposed Quantum-SVD algorithm interpolates the non-uniform angles in the Fourier domain. The error of the Quantum-SVD approach is some orders lower than the error given by ordinary Quantum Fourier Transformation. Our Quantum-SVD algorithm is a fundamentally novel approach for the computation of the Quantum Fourier Transformation (QFT) of non-uniform states. The presented Quantum-SVD algorithm is based on the singular value decomposition mechanism, and the computation of Quantum Fourier Transformation of non-uniform angles of a quantum system. The Quantum-SVD approach provides advantages in terms of computational structure, being based on QFT and multiplications.

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de Franco, Roberto, and Gemma Musacchio. "Polarization filter with singular value decomposition." GEOPHYSICS 66, no. 3 (May 2001): 932–38. http://dx.doi.org/10.1190/1.1444983.

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We present a singular value decomposition (SVD) based algorithm for polarization filtering of triaxial seismic recordings based on the assumption that the particle motion trajectory is essentially 2-D (elliptical polarization). The filter is the sum of the first two eigenimages of the SVD on the signal matrix. Weighing functions, which are strictly dependent on the intensity (linearity and planarity) of the polarization, are applied. The efficiency of the filter is tested on synthetic traces and on real data, and found to be superior to solely covariance‐based filter algorithms. Although SVD and covariance‐based methods have similar theoretical approach to the solution of the eigenvalue problem, SVD does not require any further rotation along the polarization ellipsoid principal axes. The algorithm presented here is a robust and fast filter that properly reproduces polarization attributes, amplitude, and phase of the original signal. A major novelty is the enhancement of both elliptical and linear polarized signals. Moreover as SVD preserves the amplitude ratios across the triaxial recordings, the particle motion ellipse before and after filtering retains a correct orientation, overcoming a typical artifact of the covariance‐based methods.

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Akritas, Alkiviadis G., and Gennadi I. Malaschonok. "Applications of singular-value decomposition (SVD)." Mathematics and Computers in Simulation 67, no. 1-2 (September 2004): 15–31. http://dx.doi.org/10.1016/j.matcom.2004.05.005.

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Xu, Peng Fei, Hong Bin Zhang, Xin Feng Wang, and Zheng Yong Yu. "Color Image Compression Using Block Singular Value Decomposition." Applied Mechanics and Materials 303-306 (February 2013): 2122–25. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.2122.

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This paper looks at the application of Singular Value Decomposition (SVD) to color image compression. Based on the basic principle and characteristics of SVD, combined with the image of the matrix structure. A block SVD-based image compression scheme is demonstrated and the usage feasibility of Block SVD-based image compression is proved.

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Galo, André Luiz, and Márcio Francisco Colombo. "Singular Value Decomposition and Ligand Binding Analysis." Journal of Spectroscopy 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/372596.

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Singular values decomposition (SVD) is one of the most important computations in linear algebra because of its vast application for data analysis. It is particularly useful for resolving problems involving least-squares minimization, the determination of matrix rank, and the solution of certain problems involving Euclidean norms. Such problems arise in the spectral analysis of ligand binding to macromolecule. Here, we present a spectral data analysis method using SVD (SVD analysis) and nonlinear fitting to determine the binding characteristics of intercalating drugs to DNA. This methodology reduces noise and identifies distinct spectral species similar to traditional principal component analysis as well as fitting nonlinear binding parameters. We applied SVD analysis to investigate the interaction of actinomycin D and daunomycin with native DNA. This methodology does not require prior knowledge of ligand molar extinction coefficients (free and bound), which potentially limits binding analysis. Data are acquired simply by reconstructing the experimental data and by adjusting the product of deconvoluted matrices and the matrix of model coefficients determined by the Scatchard and McGee and von Hippel equation.

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Balle, Borja, Prakash Panangaden, and Doina Precup. "Singular value automata and approximate minimization." Mathematical Structures in Computer Science 29, no. 9 (May 27, 2019): 1444–78. http://dx.doi.org/10.1017/s0960129519000094.

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AbstractThe present paper uses spectral theory of linear operators to construct approximatelyminimal realizations of weighted languages. Our new contributions are: (i) a new algorithm for the singular value decomposition (SVD) decomposition of finite-rank infinite Hankel matrices based on their representation in terms of weighted automata, (ii) a new canonical form for weighted automata arising from the SVD of its corresponding Hankelmatrix, and (iii) an algorithmto construct approximateminimizations of given weighted automata by truncating the canonical form.We give bounds on the quality of our approximation.

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Fiori, Simone. "Singular Value Decomposition Learning on Double Stiefel Manifold." International Journal of Neural Systems 13, no. 03 (June 2003): 155–70. http://dx.doi.org/10.1142/s0129065703001406.

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The aim of this paper is to present a unifying view of four SVD-neural-computation techniques found in the scientific literature and to present some theoretical results on their behavior. The considered SVD neural algorithms are shown to arise as Riemannian-gradient flows on double Stiefel manifold and their geometric and dynamical properties are investigated with the help of differential geometry.

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Audu, Khadeejah James. "Application of Singular Value Decomposition technique for compressing images." Gadau Journal of Pure and Allied Sciences 1, no. 2 (August 19, 2022): 82–94. http://dx.doi.org/10.54117/gjpas.v1i2.21.

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Image processing is becoming increasingly important as imaging technology has advanced. A storage constraint might occur even when image quality is an influential factor. This means finding a way to reduce the volume of data while still retaining quality, since compactable systems and minimal space are more desirable in the current computing field. An image compression technique that is frequently used is singular value decomposition (SVD). SVD is a challenging and promising way to loosely compress images, given how many people use images now and how many different kinds of media there are. SVD can be employed to compress digital images by approximating the matrices that generate such images, thereby saving memory while quality is affected negligibly. The technique is a great tool for lowering image dimensions. However, SVD on a large dataset might be expensive and time-consuming. The current study focuses on its improvement and implements the proposed technique in a Python environment. We illustrate the concept of SVD, apply its technique to compress an image through the use of an improved SVD process, and further compare it with some existing techniques. The proposed technique was used to test and evaluate the compression of images under various r-terms, and the singular value characteristics were incorporated into image processing. By utilization of the proposed SVD technique, it was possible to compress a large image of dimension 4928 x 3264 pixels into a reduced 342 x 231 pixels with fair quality. The result has led to better image compression in terms of size, processing time, and errors.

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Hu, Ji Chao, Hong Yan Huang, and Ai Hua Liang. "Video Watermarking Algorithm Based on DCT and SVD." Applied Mechanics and Materials 321-324 (June 2013): 2688–92. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.2688.

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This paper presents an original video based on DCT (Discrete Cosine Transform) and SVD (singular value decomposition) algorithm combined adaptive watermark embedding algorithm. Algorithm will first split the video stream into different scenes, each frame of the discrete cosine transform, and its singular value decomposition of the DC coefficient; the original watermark image and after scrambling algorithm using singular value decomposition singular value sequence, and finally watermarked image. Experiments show that the algorithm meet the invisibility requirements also meet the robustness requirements, efficiently against attacks as frame dropping, Gaussian Noise and Compression attack.

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Nadubeediramesh, Rashmi, and Aryya Gangopadhyay. "Dynamic Document Clustering Using Singular Value Decomposition." International Journal of Computational Models and Algorithms in Medicine 3, no. 3 (July 2012): 27–55. http://dx.doi.org/10.4018/jcmam.2012070103.

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Incremental document clustering is important in many applications, but particularly so in healthcare contexts where text data is found in abundance, ranging from published research in journals to day-to-day healthcare data such as discharge summaries and nursing notes. In such dynamic environments new documents are constantly added to the set of documents that have been used in the initial cluster formation. Hence it is important to be able to incrementally update the clusters at a low computational cost as new documents are added. In this paper the authors describe a novel, low cost approach for incremental document clustering. Their method is based on conducting singular value decomposition (SVD) incrementally. They dynamically fold in new documents into the existing term-document space and dynamically assign these new documents into pre-defined clusters based on intra-cluster similarity. This saves the cost of re-computing SVD on the entire document set every time updates occur. The authors also provide a way to retrieve documents based on different window sizes with high scalability and good clustering accuracy. They have tested their proposed method experimentally with 960 medical abstracts retrieved from the PubMed medical library. The authors’ incremental method is compared with the default situation where complete re-computation of SVD is done when new documents are added to the initial set of documents. The results show minor decreases in the quality of the cluster formation but much larger gains in computational throughput.

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Tzeng, Jengnan. "Split-and-Combine Singular Value Decomposition for Large-Scale Matrix." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/683053.

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The singular value decomposition (SVD) is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. Although the SVD plays an essential role in these fields, its apparent weakness is the order three computational cost. This order three computational cost makes many modern applications infeasible, especially when the scale of the data is huge and growing. Therefore, it is imperative to develop a fast SVD method in modern era. If the rank of matrix is much smaller than the matrix size, there are already some fast SVD approaches. In this paper, we focus on this case but with the additional condition that the data is considerably huge to be stored as a matrix form. We will demonstrate that this fast SVD result is sufficiently accurate, and most importantly it can be derived immediately. Using this fast method, many infeasible modern techniques based on the SVD will become viable.

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Naidu, Sivasubramaniam Nambi, and Ramesh Kumar Gupta. "Novel Attitude Estimation Of Strapdown Inertial Navigation Systems With Singular Value Decomposition Technique." Defence Science Journal 72, no. 2 (May 11, 2022): 281–89. http://dx.doi.org/10.14429/dsj.72.17637.

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Davenport’s q method & the Singular Value Decomposition (SVD) method are the two vigorous estimators that reduces Wahba’s loss function. In these, the q method is slightly quicker due to its computation of optimum quaternion as an eigenvector of a symmetric 4x4 matrix through the prevalent eigenvalue. The ESOQ and ESOQ2 (EStimators of the Optimal Quaternion) and the QUEST (QUaternion ESTimator) algorithms are less determined as the extreme eigenvalue’s distinguishing polynomial equation is solved by them. These estimators are apt to track the undulations of the sea with equivalent precision and accurateness. The SVD method is chosen and shown to be the most robust of all the hostile methods for the orientation of SDINS (Strap-Down Inertial Navigation Systems) using rate matching observations at sea in this paper. SVD is known most robust decomposition of all the decompositions of a matrix. SVD based attitude estimation being a batch technique would suffer from much less computational issues.

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KAISER, ALEXANDER, WOLFRAM SCHENCK, and RALF MÖLLER. "COUPLED SINGULAR VALUE DECOMPOSITION OF A CROSS-COVARIANCE MATRIX." International Journal of Neural Systems 20, no. 04 (August 2010): 293–318. http://dx.doi.org/10.1142/s0129065710002437.

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We derive coupled on-line learning rules for the singular value decomposition (SVD) of a cross-covariance matrix. In coupled SVD rules, the singular value is estimated alongside the singular vectors, and the effective learning rates for the singular vector rules are influenced by the singular value estimates. In addition, we use a first-order approximation of Gram-Schmidt orthonormalization as decorrelation method for the estimation of multiple singular vectors and singular values. Experiments on synthetic data show that coupled learning rules converge faster than Hebbian learning rules and that the first-order approximation of Gram-Schmidt orthonormalization produces more precise estimates and better orthonormality than the standard deflation method.

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Bekara, Maïza, and Mirko Van der Baan. "Local singular value decomposition for signal enhancement of seismic data." GEOPHYSICS 72, no. 2 (March 2007): V59—V65. http://dx.doi.org/10.1190/1.2435967.

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Singular value decomposition (SVD) is a coherency-based technique that provides both signal enhancement and noise suppression. It has been implemented in a variety of seismic applications — mostly on a global scale. In this paper, we use SVD to improve the signal-to-noise ratio of unstacked and stacked seismic sections, but apply it locally to cope with coherent events that vary with both time and offset. The local SVD technique is compared with [Formula: see text] deconvolution and median filtering on a set of synthetic and real-data sections. Local SVD is better than [Formula: see text] deconvolution and median filtering in removing background noise, but it performs less well in enhancing weak events or events with conflicting dips. Combining [Formula: see text] deconvolution or median filtering with local SVD overcomes the main weaknesses associated with each individual method and leads to the best results.

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Sundar, K. Joseph Abraham, V. Vaithiyanathan, M. Manickavasagam, and A. K. Sarkar. "Enhanced Singular Value Decomposition based Fusion for Super Resolution Image Reconstruction." Defence Science Journal 65, no. 6 (November 10, 2015): 459. http://dx.doi.org/10.14429/dsj.65.8336.

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<p>The singular value decomposition (SVD) plays a very important role in the field of image processing for applications such as feature extraction, image compression, etc. The main objective is to enhance the resolution of the image based on Singular Value Decomposition. The original image and the subsequent sub-pixel shifted image, subjected to image registration is transferred to SVD domain. An enhanced method of choosing the singular values from the SVD domain images to reconstruct a high resolution image using fusion techniques is proposesed. This technique is called as enhanced SVD based fusion. Significant improvement in the performance is observed by applying enhanced SVD method preceding the various interpolation methods which are incorporated. The technique has high advantage and computationally fast which is most needed for satellite imaging, high definition television broadcasting, medical imaging diagnosis, military surveillance, remote sensing etc.</p>

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Zheng, Min, and Fan Shen. "Performance Comparison of Dense Frequency Identifications for Empirical Mode Decomposition." Advanced Materials Research 378-379 (October 2011): 266–69. http://dx.doi.org/10.4028/www.scientific.net/amr.378-379.266.

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Empirical Mode Decomposition(EMD) suffers some difficulties in separating dense frequencies. The Wavelet Packet Transform (WPT) and Singular-Value Decomposition (SVD) as signal preprocessors were used to decompose a simulated signal with dense frequency components and the performances of two signal preprocess technologies were compared in this paper. The results show that Singular-Value Decomposition (SVD) as preprocessor was better in separating dense frequencies than Wavelet Packet Transform (WPT).

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Jackson, G. M., I. M. Mason, and S. A. Greenhalgh. "Principal component transforms of triaxial recordings by singular value decomposition." GEOPHYSICS 56, no. 4 (April 1991): 528–33. http://dx.doi.org/10.1190/1.1443068.

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Polarization analysis can be achieved efficiently by treating a time window of a single‐station triaxial recording as a matrix and doing a singular value decomposition (SVD) of this seismic data matrix. SVD of the triaxial data matrix produces an eigenanalysis of the data covariance (cross‐energy) matrix and a rotation of the data onto the directions given by the eigenanalysis (Karhunen‐Loève transform), all in one step. SVD provides a complete principal components analysis of the data in the analysis time window. Selection of this time window is crucial to the success of the analysis and is governed by three considerations: the window should contain only one arrival; the window should be such that the signal‐to‐noise ratio is maximized; and the window should be long enough to be able to discriminate random noise from signal. The SVD analysis provides estimates of signal, signal polarization directions, and noise. An F‐test is proposed which gives the confidence level for the hypothesis of rectilinear polarization. This paper illustrates the analysis and interpretation of synthetic rectilinearly and elliptically polarized arrivals at a single triaxial station by SVD.

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Mohammed K. Al-Obaidi and Anas Fouad Ahmed. "Implementation of image compression based on singular value decomposition." Global Journal of Engineering and Technology Advances 11, no. 3 (June 30, 2022): 086–92. http://dx.doi.org/10.30574/gjeta.2022.11.3.0097.

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Analyzing big data amount and the limitation of the storage data devices and the rate of data is one of the most critical issues in data processing and transferring. In this research, one of the essential approaches for image compression is proposed. Singular value decomposition (SVD) is a highly effective mathematic technique which is used for the reduction process applied to redundant data in order to minimize the required storage space or transferring channel. The main idea of this work is divided into two main phases. The first phase is explained the (SVD) computational steps approach in detailed while the second phase is described the result of the applying (SVD) in the field of image compression. The achievement results of this experiment show a powerful controlled technique depend on the desired rank of a decomposed image in order to achieve a compression result by the using of a factorized matrix on image compression. The performance of the compressed image is examined in terms of peak to signal ratio and compression ratio.

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Namayanja, Josephine M. "Evaluation of Clustering Patterns using Singular Value Decomposition (SVD)." International Journal of Computational Models and Algorithms in Medicine 1, no. 3 (July 2010): 69–80. http://dx.doi.org/10.4018/jcmam.2010070104.

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Computational techniques, such as Simple K, have been used for exploratory analysis in applications ranging from data mining research, machine learning, and computational biology. The medical domain has benefitted from these applications, and in this regard, the authors analyze patterns in individuals of selected age groups linked with the possibility of Metabolic Syndrome (MetS), a disorder affecting approximately 45% of the elderly. The study identifies groups of individuals behaving in two defined categories, that is, those diagnosed with MetS (MetS Positive) and those who are not (MetS Negative), comparing the pattern definition. The paper compares the cluster formation in patterns when using a data reduction technique referred to as Singular Value Decomposition (SVD) versus eliminating its application in clustering. Data reduction techniques like SVD have proved to be very useful in projecting only what is considered to be key relations in the data by suppressing the less important ones. With the existence of high dimensionality, the importance of SVD can be highly effective. By applying two internal measures to validate the cluster quality, findings in this study prove interesting in context to both approaches.

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Shalannanda, Wervyan, Rafi Falih Mulia, Arief Insanu Muttaqien, Naufal Rafi Hibatullah, and Annisabelia Firdaus. "Singular value decomposition model application for e-commerce recommendation system." JITEL (Jurnal Ilmiah Telekomunikasi, Elektronika, dan Listrik Tenaga) 2, no. 2 (September 30, 2022): 103–10. http://dx.doi.org/10.35313/jitel.v2.i2.2022.103-110.

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A recommendation system is one of the most important things in today’s technology. It can suggest products that match the user’s preferences. Many fields utilize this system, including e-commerce, using various algorithms. This paper used the matrix factorization-based algorithm, singular value decomposition (SVD), to make a recommendation system based on users’ similarities. Afterward, we implement the model against the ModCloth Amazon dataset. The results imply that the SVD algorithm yields the best accuracy compared to other matrix factorization-based algorithms with root mean square error (RMSE) of 1.055586. Then, we optimized the SVD algorithm by changing the hyperparameters of the algorithm to generate better accuracy and yield a model with an RMSE value of 1.041784.

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Wu, You, Lei Feng Liu, Xue Liang Zhao, and Kun Hua Zhong. "Implementation of SVD Parallel Algorithm and its Application in Medical Industry." Applied Mechanics and Materials 743 (March 2015): 515–21. http://dx.doi.org/10.4028/www.scientific.net/amm.743.515.

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Singular value decomposition (SVD) is an important part of the numerical calculateion.It is widely used in biology, meteorology, quantum mechanics and other fields. It is discovered that the speed of calculation and accuracy has become the two basic questions of singular value decomposition during the construction process. With the era of big data,there are more and more cases of largescale data analysis using SVD. Singular value decomposition was originally an algorithm for computing resources are consumed, if still using the traditional stand-alone mode, will consume a lot of time cost. In order to improve the computing speed and accuracy, the system implement the parallel SVD algorithm which is based on unilateral jacobi method.It is used to analyze large-scale matrix about medicine for finding similarity of medicine efficacy.

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Patel, Ibrahim, Raghavendra Kulkarni, and Dr P. Nageswar Rao. "Robust Singular Value Decomposition Algorithm for Unique Faces." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 4, no. 2 (June 21, 2018): 596–603. http://dx.doi.org/10.24297/ijct.v4i2c1.4178.

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It has been read and also seen by physical encounters that there found to be seven near resembling humans by appearance .Many a times one becomes confused with respect to identification ofÂ such near resembling faces when one encounters them. TheÂ recognitionÂ ofÂ familiarÂ facesÂ playsÂ aÂ fundamentalÂ roleÂ inÂ ourÂ social interactions. HumansÂ areÂ ableÂ toÂ identifyÂ reliablyÂ aÂ largeÂ numberÂ ofÂ facesÂ and psychologistsÂ areÂ interestedÂ inÂ understandingÂ theÂ perceptualÂ andÂ cognitive mechanismsÂ atÂ theÂ baseÂ ofÂ theÂ faceÂ recognitionÂ process. As it is needed that an automated face recognition system should be faces specific, it should effectively use features that discriminate a face from others by preferably amplifying distinctive characteristics of face. Face recognition has drawn wide attention from researchers in areas of machine learning, computer vision, pattern recognition, neural networks, access control, information security, law enforcement and surveillance, smart cards etc. The paper shows that the most resembling faces can be recognized by having a unique value per face under different variations. Certain image transformations, such as intensity negation, strange viewpoint changes,Â andÂ changesÂ inÂ lightingÂ directionÂ canÂ severelyÂ disruptÂ humanÂ face recognition. It has been said again and again by research scholars that SVD algorithm is not good enough to classify faces under large variations but this paper proves that the SVD algorithm is most robust algorithm and can be proved effective in identifying faces under large variations as applicable to unique faces. This paper works on these aspects and tries to recognize the unique faces by applying optimized SVD algorithm.

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Worsley, Keith J., Jen-I. Chen, Jason Lerch, and Alan C. Evans. "Comparing functional connectivity via thresholding correlations and singular value decomposition." Philosophical Transactions of the Royal Society B: Biological Sciences 360, no. 1457 (May 29, 2005): 913–20. http://dx.doi.org/10.1098/rstb.2005.1637.

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We compare two common methods for detecting functional connectivity: thresholding correlations and singular value decomposition (SVD). We find that thresholding correlations are better at detecting focal regions of correlated voxels, whereas SVD is better at detecting extensive regions of correlated voxels. We apply these results to resting state networks in an fMRI dataset to look for connectivity in cortical thickness.

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Berry, Michael W. "Large-Scale Sparse Singular Value Computations." International Journal of Supercomputing Applications 6, no. 1 (April 1992): 13–49. http://dx.doi.org/10.1177/109434209200600103.

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We present four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture. We emphasize Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left- and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography. The target architectures for our implementations are the CRAY-2S/4–128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices. This research may help advance the development of future out-of-core sparse SVD methods, which can be used, for example, to handle extremely large sparse matrices 0 × (106) rows or columns associated with extremely large databases in query-based information-retrieval applications.

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Wu, Feng-Jih, Chih-Ju Chou, Ying Lu, and Jarm-Long Chung. "Modeling Electromechanical Overcurrent Relays Using Singular Value Decomposition." Journal of Applied Mathematics 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/104952.

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This paper presents a practical and effective novel approach to curve fit electromechanical (EM) overcurrent (OC) relay characteristics. Based on singular value decomposition (SVD), the curves are fitted with equation in state space under modal coordinates. The relationships between transfer function and Markov parameters are adopted in this research to represent the characteristic curves of EM OC relays. This study applies the proposed method to two EM OC relays: the GE IAC51 relay with moderately inverse-time characteristic and the ABB CO-8 relay with inverse-time characteristic. The maximum absolute values of errors of hundreds of sample points taken from four time dial settings (TDS) for each relay between the actual characteristic curves and the corresponding values from the curve-fitting equations are within the range of 10 milliseconds. Finally, this study compares the SVD with the adaptive network and fuzzy inference system (ANFIS) to demonstrate its accuracy and identification robustness.

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Lei, Xiujun, Jie Guo, and Chang’an Zhu. "Vision-Based Faint Vibration Extraction Using Singular Value Decomposition." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/306865.

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Vibration measurement is important for understanding the behavior of engineering structures. Unlike conventional contact-type measurements, vision-based methodologies have attracted a great deal of attention because of the advantages of remote measurement, nonintrusive characteristic, and no mass introduction. It is a new type of displacement sensor which is convenient and reliable. This study introduces the singular value decomposition (SVD) methods for video image processing and presents a vibration-extracted algorithm. The algorithms can successfully realize noncontact displacement measurements without undesirable influence to the structure behavior. SVD-based algorithm decomposes a matrix combined with the former frames to obtain a set of orthonormal image bases while the projections of all video frames on the basis describe the vibration information. By means of simulation, the parameters selection of SVD-based algorithm is discussed in detail. To validate the algorithm performance in practice, sinusoidal motion tests are performed. Results indicate that the proposed technique can provide fairly accurate displacement measurement. Moreover, a sound barrier experiment showing how the high-speed rail trains affect the sound barrier nearby is carried out. It is for the first time to be realized at home and abroad due to the challenge of measuring environment.

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Kwarteng, Asenso, and Yaw Marfo. "Radar Signals Compression using Singular Value Decomposition (SVD) Approach." International Journal of Computer Applications 150, no. 12 (September 22, 2016): 14–19. http://dx.doi.org/10.5120/ijca2016911426.

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Savolainen, Sauli E., and B. Kristian Liewendahl. "Analysis of scintigrams by singular value decomposition (SVD) technique." Annals of Nuclear Medicine 8, no. 2 (June 1994): 101–8. http://dx.doi.org/10.1007/bf03165014.

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Wu, Liang, Qian Xu, Janne Heikkilä, Zijun Zhao, Liwei Liu, and and Yali Niu. "A Star Sensor On-Orbit Calibration Method Based on Singular Value Decomposition." Sensors 19, no. 15 (July 26, 2019): 3301. http://dx.doi.org/10.3390/s19153301.

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The navigation accuracy of a star sensor depends on the estimation accuracy of its optical parameters, and so, the parameters should be updated in real time to obtain the best performance. Current on-orbit calibration methods for star sensors mainly rely on the angular distance between stars, and few studies have been devoted to seeking new calibration references. In this paper, an on-orbit calibration method using singular values as the calibration reference is introduced and studied. Firstly, the camera model of the star sensor is presented. Then, on the basis of the invariance of the singular values under coordinate transformation, an on-orbit calibration method based on the singular-value decomposition (SVD) method is proposed. By means of observability analysis, an optimal model of the star combinations for calibration is explored. According to the physical interpretation of the singular-value decomposition of the star vector matrix, the singular-value selection for calibration is discussed. Finally, to demonstrate the performance of the SVD method, simulation calibrations are conducted by both the SVD method and the conventional angular distance-based method. The results show that the accuracy and convergence speed of both methods are similar; however, the computational cost of the SVD method is heavily reduced. Furthermore, a field experiment is conducted to verify the feasibility of the SVD method. Therefore, the SVD method performs well in the calibration of star sensors, and in particular, it is suitable for star sensors with limited computing resources.

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Luo, Dijun, Chris Ding, and Heng Huang. "Multi-Level Cluster Indicator Decompositions of Matrices and Tensors." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (August 4, 2011): 423–28. http://dx.doi.org/10.1609/aaai.v25i1.7933.

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A main challenging problem for many machine learning and data mining applications is that the amount of data and features are very large, so that low-rank approximations of original data are often required for efficient computation. We propose new multi-level clustering based low-rank matrix approximations which are comparable and even more compact than Singular Value Decomposition (SVD). We utilize the cluster indicators of data clustering results to form the subspaces, hence our decomposition results are more interpretable. We further generalize our clustering based matrix decompositions to tensor decompositions that are useful in high-order data analysis. We also provide an upper bound for the approximation error of our tensor decomposition algorithm. In all experimental results, our methods significantly outperform traditional decomposition methods such as SVD and high-order SVD.

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Sumiah, Aah, and Yan Alfian. "Implementasi Watermarking pada Citra Digital dengan Metode Singular Value Decomposition (svd)." JEJARING : Jurnal Teknologi dan Manajemen Informatika 6, no. 1 (May 6, 2021): 1–6. http://dx.doi.org/10.25134/jejaring.v6i1.6720.

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Today computers have been used in all aspects of life as a means of processing digital data. The Development of computer makes digital files mostly used because the computer is an electronic equipment used to process digital file. Moreover with network technology developments internet it enables file exchange and process the file.This ease impacts to copyright, so that needs to be considered the protection of copyrights. Such protection insertion namely with a proprietary identity against certain files.one of them is watermarking technique. There are several techniques of digital watermarking which have developed. One technique is digital watermark image on singular value decomposition (svd), ie insertion a singular image. Watermarking method using singular value decomposition (svd) leads the overall in scattered watermark image, so that when the slightest changes occurred on with easy image can be known. In addition itu resistant against different attacks, such as croping, rotation changes. The author discusses about the digital image watermarking based svd. In making application he uses delphi 7.Keywords: Digital Image, Watermarking, Singular Value Decomposition.

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Utami, Bernadhita Herindri Samodera, Trisnawati Trisnawati, Rani Pratiwi, and Miswan Gumanti. "Robust Singular Value Decomposition Method on Minor Outlier Data." Jurnal Varian 4, no. 1 (September 29, 2020): 19–24. http://dx.doi.org/10.30812/varian.v4i1.857.

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In multivariate statistics, Singular Value Decomposition (SVD) for a data matrix containing outliers does not provide data that can be analyzed optimally. This study aims to overcome outlier data using the Robust Singular Value Decomposition (RSVD) method and compare it with the SVD method. The analysis using the RSVD method includes several steps, namely determining the initial predictive value of the vector u and regressing it then normalizing the estimator vector β and carrying out the iteration process until convergent results are obtained. The results of this study indicate that the RSVD for dealing with minor outliers data is not influenced by initial estimates. The RSVD method is strongly influenced by the large amount of outliers data, the more extreme outliers data, the more iterations are.

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Aswani Kumar, Ch, and Ramaraj Palanisamy. "Comparison of Matrix Dimensionality Reduction Methods in Uncovering Latent Structures in the Data." Journal of Information & Knowledge Management 09, no. 01 (March 2010): 81–92. http://dx.doi.org/10.1142/s0219649210002498.

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Matrix decomposition methods: Singular Value Decomposition (SVD) and Semi Discrete Decomposition (SDD) are proved to be successful in dimensionality reduction. However, to the best of our knowledge, no empirical results are presented and no comparison between these methods is done to uncover latent structures in the data. In this paper, we present how these methods can be used to identify and visualise latent structures in the time series data. Results on a high dimensional dataset demonstrate that SVD is more successful in uncovering the latent structures.

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Dong, Yu Hua, and Hai Chun Ning. "Exterior Ballistic Data Processing by SVD and Wavelet Transform." Advanced Materials Research 562-564 (August 2012): 1394–97. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.1394.

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This paper proposes a method of wavelet transform combined with SVD (Singular Value Extracting), and the abnormal data elimination in its trajectory measurement is studied. After the wavelet decomposition of the observed data, combining the approximate component and the detail component, the phase space is reconstructed. The increment criterion of singular entropy is used for the input observed matrix of SVD, and the singular value is selected. Then the original signal is reconstructed by SVD inverse transform. This method overcomes the distortion problem of data end in phase space reconstruction by Hankel matrix. The reconstructed phase space by components of wavelet decomposition is orthogonal. So it further improves the accuracy of noise reduction and abnormal detection by SVD. The results of experimental data processing show the effectiveness of this method proposed in the paper.

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Hou, Gao Yan, Yong Lv, Hao Huang, and Yi Zhu. "A Feature Extraction Method of Gear Fault Based on the SVD EMD and Morphology." Applied Mechanics and Materials 433-435 (October 2013): 477–82. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.477.

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In order to extract the weak signal from strong background signal characteristics, a feature extraction method combined of the singular value decomposition (SVD), empirical mode decomposition (EMD) and mathematical morphology was proposed. The signal got through the singular value decomposition first. Next took the average value of the decomposed main components. And carried on the empirical mode decomposition and selected the main component to summate and refactor. Then morphological difference filter was used to extract the frequency characteristics of the fault signal. The results of numerical simulation test and gear fault simulation experiments show that the proposed method can clearly extract the frequency characteristics of weak signal from strong background signal and noise. Comparison has been done with the results of singular value decomposition (SVD) and morphological filtering method and empirical mode decomposition form of filtering method. It proves the effectiveness of the proposed method.

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Widodo, Widodo, and Durra Handri Saputera. "Improving Levenberg-Marquardt Algorithm Inversion Result Using Singular Value Decomposition." Earth Science Research 5, no. 2 (April 8, 2016): 20. http://dx.doi.org/10.5539/esr.v5n2p20.

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Inversion is a process to determine model parameters from data. In geophysics this process is very important because subsurface image is obtained from this process. There are many inversion algorithms that have been introduced and applied in geophysics problems; one of them is Levenberg-Marquardt (LM) algorithm. In this paper we will present one of LM algorithm application in one-dimensional magnetotelluric (MT) case. The LM algorithm used in this study is improved version of LM algorithm using singular value decomposition (SVD). The result from this algorithm is then compared with the algorithm without SVD in order to understand how much it has been improved. To simplify the comparison, simple synthetic model is used in this study. From this study, the new algorithm can improve the result of the original LM algorithm. In addition, SVD is allowing more parameter analysis to be done in its process. The algorithm created from this study is then used in our modeling program, called MAT1DMT.

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Valverde-Albacete, Francisco, and Carmen Peláez-Moreno. "The Singular Value Decomposition over Completed Idempotent Semifields." Mathematics 8, no. 9 (September 12, 2020): 1577. http://dx.doi.org/10.3390/math8091577.

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In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their instances—the complete schedule algebra or completed max-plus semifield, the tropical algebra, and the max-times algebra—are useful in a range of applications, e.g., morphological processing. We further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields (K-FCA) started in a prior work. We find out that for a matrix with entries considered in a complete idempotent semifield, the Galois connection at the heart of K-FCA provides two basis of left- and right-singular vectors to choose from, for reconstructing the matrix. These are join-dense or meet-dense sets of object or attribute concepts of the concept lattice created by the connection, and they are almost surely not pairwise orthogonal. We conclude with an attempt analogue of the fundamental theorem of linear algebra that gathers all results and discuss it in the wider setting of matrix factorization.

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Zhao, Yi, and Marius Schmidt. "New software for the singular value decomposition of time-resolved crystallographic data." Journal of Applied Crystallography 42, no. 4 (June 30, 2009): 734–40. http://dx.doi.org/10.1107/s0021889809019050.

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Singular value decomposition (SVD) has been successfully used in the analysis of time-resolved crystallographic data. A new software package for Linux-based operating systems, calledSVD4TX, has been developed. In contrast to an earlier version of the SVD program, written in Fortran, the new program provides a GTK+-based graphical user interface for easy user guidance through the entire SVD process. New features, such as an improved, more stable routine to determine a compatible kinetic mechanism, are implemented in theSVD4TXprogram package so that it provides almost all the necessary tools for a semi-automatic and effective SVD-based analysis of time-resolved crystallographic data in one program package.

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Faßbender, Heike, and Martin Halwaß. "On the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices." Special Matrices 8, no. 1 (January 2, 2020): 1–13. http://dx.doi.org/10.1515/spma-2020-0001.

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AbstractThe singular values σ > 1 of an n × n involutory matrix A appear in pairs (σ, {1 \over \sigma }). Their left and right singular vectors are closely connected. The case of singular values σ = 1 is discussed in detail. These singular values may appear in pairs (1,1) with closely connected left and right singular vectors or by themselves. The link between the left and right singular vectors is used to reformulate the singular value decomposition (SVD) of an involutory matrix as an eigendecomposition. This displays an interesting relation between the singular values of an involutory matrix and its eigenvalues. Similar observations hold for the SVD, the singular values and the coneigenvalues of (skew-)coninvolutory matrices.

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Muhammed, H. A., A. A. Ayorinde, F. O. Okewole, M. A. Adelabu, and A. I. Mowete. "Singular Value Decomposition and Quasi-Moment-Method as pathloss model calibration alternatives." Nigerian Journal of Technology 41, no. 3 (November 2, 2022): 483–504. http://dx.doi.org/10.4314/njt.v41i3.8.

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Using indoor-to-outdoor pathloss measurements for a femtocell network, this paper presents a comparative evaluation of the performances of Singular Value Decomposition (SVD) and Quasi-Moment-Method (QMM) as pathloss model calibration tools. First, the performances of two published SVD models are compared with those of corresponding QMM models, developed through the calibration of basic ECC33 and WINNER II models. Then, and after noting that the ‘base models’ from which the poorer performing, published SVD calibrations reportedly derive, are either incompletely described or characterized by misprints, alternative ‘base models’ are prescribed by this paper. It is then shown through analysis that QMM and SVD represent alternative implementations of the same basic model calibration algorithm. Computational results due to the alternative models suggest that better performance metrics (Mean Prediction Error (MPE) and Root Mean Square Prediction Error (RMSPE)) are recorded, when existing basic models are modified to mimic the SVD ‘base model’, prior to SVD/QMM calibration. Indeed, because the MPE due to the calibration of the alternative models are all close to zero (actually equal to zero in a few cases), the associated residual profiles closely follow the Gaussian distribution typically assumed in the literature, for shadow fading modelling.

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Et. al., Geluvaraj B,. "AMatrix factorization technique using parameter tuning of singular value decomposition for Recommender Systems." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (April 10, 2021): 3313–19. http://dx.doi.org/10.17762/turcomat.v12i2.2390.

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In this article we explained the concepts of SVD and algorithm evolution. MF technique and the working of it with computational formulas. PCA withstep-by-step approach with example and A novel approach of Hyper SVD and How to fine tune it and pseudocode of the Hyper SVD with the Experimental setup using SurpriseLib and computing RMSE and MSE for the accuracy purpose and solving with the real time example which solves the cold start hassle also together and it can be seen that comparison of SVD and Hyper SVD and Random algorithm is done and types of Movies they recommended. There is far more difference between the results of the both algorithms and movie recommendations as per the results Hyper SVD is flexible and efficient and superior compared to other algorithms.

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Huang, Chenguang, Jianhui Lin, Jianming Ding, and Yan Huang. "A Novel Wheelset Bearing Fault Diagnosis Method Integrated CEEMDAN, Periodic Segment Matrix, and SVD." Shock and Vibration 2018 (November 5, 2018): 1–18. http://dx.doi.org/10.1155/2018/1382726.

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A novel fault diagnosis method, named CPS, is proposed based on the combination of CEEMDAN (complete ensemble empirical mode decomposition with adaptive noise), PSM (periodic segment matrix), and SVD (singular value decomposition). Firstly, the collected vibration signals are decomposed into a set of IMFs using CEEMDAN. Secondly, the PSM of the selected IMFs is constructed. Thirdly, singular values are obtained by SVD conducted on the space of PSM. Fourthly, the impulse components are enhanced by the singular value reconstruction with the first maximal singular value. Finally, the squared envelope spectra of the reconstructed signals are used to diagnose the wheelset bearing faults. The effectiveness of the proposed CPS has been verified by simulations and experiments. Compared to the well-known Hankel-based SVD, the proposed CPS performs better at extracting the weak periodic impulse responses from the measured signals with strong noise and interferences.

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Sun, Zhenlong, Jing Yang, and Xiaoye Li. "Differentially Private Singular Value Decomposition for Training Support Vector Machines." Computational Intelligence and Neuroscience 2022 (March 26, 2022): 1–11. http://dx.doi.org/10.1155/2022/2935975.

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Support vector machine (SVM) is an efficient classification method in machine learning. The traditional classification model of SVMs may pose a great threat to personal privacy, when sensitive information is included in the training datasets. Principal component analysis (PCA) can project instances into a low-dimensional subspace while capturing the variance of the matrix A as much as possible. There are two common algorithms that PCA uses to perform the principal component analysis, eigenvalue decomposition (EVD) and singular value decomposition (SVD). The main advantage of SVD compared with EVD is that it does not need to compute the matrix of covariance. This study presents a new differentially private SVD algorithm (DPSVD) to prevent the privacy leak of SVM classifiers. The DPSVD generates a set of private singular vectors that the projected instances in the singular subspace can be directly used to train SVM while not disclosing privacy of the original instances. After proving that the DPSVD satisfies differential privacy in theory, several experiments were carried out. The experimental results confirm that our method achieved higher accuracy and better stability on different real datasets, compared with other existing private PCA algorithms used to train SVM.

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Danforth, Christopher M., and Eugenia Kalnay. "Using Singular Value Decomposition to Parameterize State-Dependent Model Errors." Journal of the Atmospheric Sciences 65, no. 4 (April 1, 2008): 1467–78. http://dx.doi.org/10.1175/2007jas2419.1.

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Abstract The purpose of the present study is to use a new method of empirical model error correction, developed by Danforth et al. in 2007, based on estimating the systematic component of the nonperiodic errors linearly dependent on the anomalous state. The method uses singular value decomposition (SVD) to generate a basis of model errors and states. It requires only a time series of errors to estimate covariances and uses negligible additional computation during a forecast integration. As a result, it should be suitable for operational use at a relatively small computational expense. The method is tested with the Lorenz ’96 coupled system as the truth and an uncoupled version of the same system as a model. The authors demonstrate that the SVD method explains a significant component of the effect that the model’s unresolved state has on the resolved state and shows that the results are better than those obtained with Leith’s empirical correction operator. The improvement is attributed to the fact that the SVD truncation effectively reduces sampling errors. Forecast improvements of up to 1000% are seen when compared with the original model. The improvements come at the expense of weakening ensemble spread.

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Reitberger, Günther, and Tomas Sauer. "Background Subtraction using Adaptive Singular Value Decomposition." Journal of Mathematical Imaging and Vision 62, no. 8 (June 5, 2020): 1159–72. http://dx.doi.org/10.1007/s10851-020-00967-4.

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Abstract An important task when processing sensor data is to distinguish relevant from irrelevant data. This paper describes a method for an iterative singular value decomposition that maintains a model of the background via singular vectors spanning a subspace of the image space, thus providing a way to determine the amount of new information contained in an incoming frame. We update the singular vectors spanning the background space in a computationally efficient manner and provide the ability to perform blockwise updates, leading to a fast and robust adaptive SVD computation. The effects of those two properties and the success of the overall method to perform a state-of-the-art background subtraction are shown in both qualitative and quantitative evaluations.

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Lakshmi, M. Naga, and Dr K. Sandhya Rani. "PRIVACY PRESERVING CLUSTERING BASED ON SINGULAR VALUE DECOMPOSITION AND GEOMETRIC DATA PERTURBATION." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 10, no. 3 (August 5, 2013): 1427–33. http://dx.doi.org/10.24297/ijct.v10i3.3272.

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Privacy preservation is a major concern when the application of data mining techniques to large repositories of data consists of personal, sensitive and confidential information. Singular Value Decomposition (SVD) is a matrix factorization method, which can produces perturbed data by efficiently removing unnecessary information for data mining. In this paper two hybrid methods are proposed which takes the advantage of existing techniques SVD and geometric data transformations in order to provide better privacy preservation. Reflection data perturbation and scaling data perturbation are familiar geometric data transformation methods which retains the statistical properties in the dataset. In hybrid method one, SVD and scaling data perturbation are used as a combination to obtain the distorted dataset. In hybrid method two, SVD and reflection data perturbation methods are used as a combination to obtain the distorted dataset. The experimental results demonstrated that the proposed hybrid methods are providing higher utility without breaching privacy.

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Journal articles on the topic 'Singular-Value Decomposition (SVD)'

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