scholarly journals НАСЛЕДОВАНИЕ СИНГУЛЯРНЫХ ВЕКТОРОВ ПРИ ПОПОЛНЕНИИ МАТРИЦЫ СТОЛБЦОМ

2021 ◽  
Vol 6 (12(81)) ◽  
pp. 36-40
Author(s):  
В. Кутрунов ◽  
Т. Латфуллин
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Symmetric Matrices ◽  
Singular Vectors ◽  
The Matrix ◽  
Singular Value Decompositions ◽  
Singular Numbers ◽  
The Right ◽  
Value Decomposition

Let the matrix A1 be obtained from the matrix A by adding a column to it on the right. The possibility of inheritance of singular numbers and the corresponding singular vectors when passing from matrix A to matrix A1 is investigated. The singular value decompositions of the matrix A are based on the scalar and vector properties of the square symmetric matrices ATA and AAT. The article deals with the singular value decomposition of the matrix A, which has more rows than columns, and the decomposition is based on the analysis of the ATA matrix.

scholarly journals A Note on Full-Rank Factorization of Matrix

2019 ◽  
Vol 15 (2) ◽  
pp. 152-154
Author(s):  
Gyan Bahadur Thapa ◽  
J. López-Bonilla ◽  
R. López-Vázquez
Keyword(s):  
Singular Value Decomposition ◽  
Full Rank ◽  
Singular Value ◽  
The Matrix ◽  
Rank Factorization ◽  
Value Decomposition

We exhibit that the Singular Value Decomposition of a matrix Anxm implies a natural full-rank factorization of the matrix.

Fault feature extraction and classification based on WPT and SVD: Application to element bearings with artificially created faults under variable conditions

2016 ◽  
Vol 231 (22) ◽  
pp. 4186-4196 ◽  
Author(s):  
Mourad Kedadouche ◽  
Zhaoheng Liu
Keyword(s):  
Support Vector Machine ◽  
Singular Value Decomposition ◽  
Wavelet Packet ◽  
Rolling Bearing ◽  
Wavelet Packet Transform ◽  
Singular Value ◽  
Support Vector ◽  
Rolling Bearings ◽  
The Matrix ◽  
Value Decomposition

Achieving a precise fault diagnosis for rolling bearings under variable conditions is a problematic challenge. In order to enhance the classification and achieves a higher precision for diagnosing rolling bearing degradation, a hybrid method is proposed. The method combines wavelet packet transform, singular value decomposition and support vector machine. The first step of the method is the decomposition of the signal using wavelet packet transform and then instantaneous amplitudes and energy are computed for each component. The Second step is to apply the singular value decomposition to the matrix constructed by the instantaneous amplitudes and energy in order to reduce the matrix dimension and obtaining the fault feature unaffected by the operating condition. The features extracted by singular value decomposition are then used as an input to the support vector machine in order to recognize the fault mode of rolling bearings. The method is applied to a bearing with faults created using electro-discharge machining under laboratory conditions. Test results show that the proposed methodology is effective to classify rolling bearing faults with high accuracy.

scholarly journals Split-and-Combine Singular Value Decomposition for Large-Scale Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jengnan Tzeng
Keyword(s):  
Singular Value Decomposition ◽  
Large Scale ◽  
Semantic Analysis ◽  
Computational Cost ◽  
Matrix Decomposition ◽  
Singular Value ◽  
Fast Method ◽  
The Matrix ◽  
Scale Matrix ◽  
Value Decomposition

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.

Color Image Compression Using Block Singular Value Decomposition

2013 ◽  
Vol 303-306 ◽  
pp. 2122-2125
Author(s):  
Peng Fei Xu ◽  
Hong Bin Zhang ◽  
Xin Feng Wang ◽  
Zheng Yong Yu
Keyword(s):  
Singular Value Decomposition ◽  
Image Compression ◽  
Basic Principle ◽  
Color Image ◽  
Singular Value ◽  
Matrix Structure ◽  
Compression Scheme ◽  
The Matrix ◽  
Value Decomposition ◽  
Color Image Compression

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.

scholarly journals Analisis Biplot pada Pemetaan Karakteristik Indeks Pembangunan Manusia (IPM) Kabupaten/Kota di Provinsi Jawa Timur tahun 2016

2018 ◽  
Vol 11 (2) ◽  
pp. 17-22
Author(s):  
Artanti Indrasetianingsih
Keyword(s):  
Singular Value Decomposition ◽  
Goodness Of Fit ◽  
Economic Education ◽  
Singular Value ◽  
Infant Mortality Rate ◽  
Poor People ◽  
Drinking Water Source ◽  
Summary Table ◽  
The Matrix ◽  
Value Decomposition

Characteristics of a region is a feature that is owned by the area. Characteristics can be seen from several aspects that exist in each region. East Java Province is a province located in the east of Java Island with Surabaya City as the Capital of Province. Biplot is one attempt to describe the data contained in the summary table in the two-dimensional graph. This analysis aims to model a matrix by overlapping vectors representing row vectors with vectors representing the vectors of the matrix column. Biplot analysis is based on the analysis of the main component (PCA biplot), ie by describing singular value or singular value decomposition (SVD). SVD aims to decipher the singular value of a matrix which is an nxp sized matrix that has been corrected with the mean and then raised the matrix and. The data used in this study using secondary data obtained from the Central Bureau of Statistics of East Java Province in 2016. Based on the result of data analysis, it can be concluded that 2 main factors are economic education consisting of infant mortality rate (X1), percentage of poor people (X2), per capita expenditure per year (X3), old school expectancy (X4) average of school length (X5) and social health factors consisted of percentage of population with appropriate drinking water source (X11), percentage of households living clean and healthy (X13).Goodness of fit biplot in economic education factor of 0.878.   Karakteristik suatu wilayah merupakan ciri yang dimiliki oleh daerah tersebut. Karakteristik dapat dilihat dari beberapa aspek di masing-masing wilayah. Provinsi Jawa Timur merupakan sebuah provinsi di sebelah timur Pulau Jawa dengan Kota Surabaya sebagai Ibukota Provinsi. Biplot adalah salah satu upaya menggambarkan data-data yang ada pada tabel ringkasan dalam grafik berdimensi dua. Analisis ini bertujuan memperagakan suatu matriks dengan menumpang tindihkan vektor-vektor yang merepresentasikan vektor-vektor baris dengan vektor-vektor yang merepresentasikan vektor-vektor kolom matriks tersebut. Analisis biplot didasarkan pada analisis komponen utama (PCA biplot), yaitu dengan menguraikan nilai singular atau singular value decomposition (SVD). Data yang digunakan pada penelitian ini menggunakan data sekunder yang diperoleh dari Badan Pusat Statistik Provinsi Jawa Timur tahun 2016. Berdasarkan hasil analisis data maka dapat disimpulkan bahwa terbentuk 2 faktor utama yaitu faktor pendidikan ekonomi yang terdiri dari variabel angka kematian bayi (X1), persentase penduduk miskin (X2), pengeluaran per kapita per tahun (X3), harapan lama sekolah (X4), rata-rata lama sekolah (X5) dan faktor sosial kesehatan terdiri dari variabel persentase penduduk dengan sumber air minum layak (X11), persentase rumah tangga berperilaku hidup bersih dan sehat (X13). Goodness of fit biplot dalam faktor pendidikan ekonomi sebesar 87,8%.  

scholarly journals The Singular Value Decomposition over Completed Idempotent Semifields

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1577
Author(s):  
Francisco Valverde-Albacete ◽  
Carmen Peláez-Moreno
Keyword(s):  
Singular Value Decomposition ◽  
Concept Lattice ◽  
Singular Value ◽  
Morphological Processing ◽  
Formal Concept ◽  
Complete Lattices ◽  
The Matrix ◽  
Dense Sets ◽  
Left And Right ◽  
Value Decomposition

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.

scholarly journals An Elementary Proof of Bevan's Theorem on the Growth of Grid Classes of Permutations

2019 ◽  
Vol 62 (4) ◽  
pp. 975-984
Author(s):  
Michael Albert ◽  
Vincent Vatter
Keyword(s):  
Growth Rate ◽  
Singular Value Decomposition ◽  
Hadamard Product ◽  
Elementary Proof ◽  
Singular Value ◽  
Stirling’S Formula ◽  
Real Numbers ◽  
Singular Vectors ◽  
Value Decomposition ◽  
Method Of Lagrange Multipliers

AbstractBevan established that the growth rate of a monotone grid class of permutations is equal to the square of the spectral radius of a related bipartite graph. We give an elementary and self-contained proof of a generalization of this result using only Stirling's formula, the method of Lagrange multipliers, and the singular value decomposition of matrices. Our proof relies on showing that the maximum over the space of n × n matrices with non-negative entries summing to one of a certain function of those entries, parametrized by the entries of another matrix Γ of non-negative real numbers, is equal to the square of the largest singular value of Γ and that the maximizing point can be expressed as a Hadamard product of Γ with the tensor product of singular vectors for its greatest singular value.

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