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Name of two different techniques based on the singular value decomposition
algebra, the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD). The
Generalized singular value decomposition
Generalized_singular_value_decomposition
Matrix decomposition
m\times n} matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an m × n {\displaystyle m\times n} complex
Singular_value_decomposition
Tensor decomposition
algebra, the higher-order singular value decomposition (HOSVD) is a misnomer. There does not exist a single tensor decomposition that retains all the defining
Higher-order singular value decomposition
Higher-order_singular_value_decomposition
Regularization technique for ill-posed problems
regularized problem. For the generalized case, a similar representation can be derived using a generalized singular-value decomposition. Finally, it is related
Ridge_regression
Representation of a matrix as a product
the singular value decomposition. Hence, the existence of the polar decomposition is equivalent to the existence of the singular value decomposition. Applicable
Matrix_decomposition
Result about when a matrix can be diagonalized
of normal matrices below). The spectral decomposition is a special case of the singular value decomposition, which states that any matrix A ∈ C m × n
Spectral_theorem
Algorithms for matrix decomposition
increase the rank, new components can be discovered using the generalized singular value decomposition. To decrease the rank, pairs of components may be greedily
Non-negative matrix factorization
Non-negative_matrix_factorization
eigenvalues. SVD contains solvers for the singular value decomposition as well as the generalized singular value decomposition. Solvers based on the cross-product
SLEPc
Most widely known generalized inverse of a matrix
pseudoinverse is by using the singular value decomposition. If A = U Σ V ∗ {\displaystyle A=U\Sigma V^{*}} is the singular value decomposition of A {\displaystyle
Moore–Penrose_inverse
Matrix factorisation in mathematics
spectral decomposition. In particular, if A is positive definite, the Schur decomposition of A, its spectral decomposition, and its singular value decomposition
Schur_decomposition
Method of decomposing a set of matrices via low-rank approximation
In linear algebra, two-dimensional singular-value decomposition (2DSVD) computes the low-rank approximation of a set of matrices such as 2D images or weather
Two-dimensional singular-value decomposition
Two-dimensional_singular-value_decomposition
Quantum algorithm framework
whose singular value decomposition is A = W Σ V † {\displaystyle A=W\Sigma V^{\dagger }} where Σ {\displaystyle \Sigma } are the singular values of A Input:
Quantum singular value transformation
Quantum_singular_value_transformation
Generalized matrix decomposition for Lie groups and Lie algebras
structure theory and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to
Cartan_decomposition
Matrix decomposition
transformation Jordan normal form List of matrices Matrix decomposition Singular value decomposition Sylvester's formula Golub, Gene H.; Van Loan, Charles
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Type of matrix representation
behind the construction of the polar decomposition is similar to that used to compute the singular-value decomposition. If A {\displaystyle A} is normal
Polar_decomposition
Process in algebra
fields. The main tensor decompositions are: Tensor rank decomposition; Higher-order singular value decomposition; Tucker decomposition; matrix product states
Tensor_decomposition
Decomposition in multilinear algebra
variation of the CP decomposition. Another popular generalization of the matrix SVD known as the higher-order singular value decomposition computes orthonormal
Tensor_rank_decomposition
Physicist and geneticist
Orly; Brown, Patrick O.; Botstein, David (18 March 2003). "Generalized singular value decomposition for comparative analysis of genome-scale expression data
Orly_Alter
Matrix decomposition
In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of
QR_decomposition
Dimensionality reduction algorithm
Eigenvalue decomposition Empirical mode decomposition Global mode Normal mode Proper orthogonal decomposition Singular-value decomposition Schmid, Peter
Dynamic_mode_decomposition
Type of matrix factorization
matrix multiplication and matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix
LU_decomposition
Matrix decomposition method
linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite
Cholesky_decomposition
Method of data analysis
multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (invented in the last quarter
Principal_component_analysis
Concepts from linear algebra
normal form and therefore admits a basis of generalized eigenvectors and a decomposition into generalized eigenspaces. In the Hermitian case, eigenvalues
Eigenvalues_and_eigenvectors
Tensor decomposition
analysis it may actually be generalized to higher mode analysis, which is also called higher-order singular value decomposition (HOSVD) or the M-mode SVD
Tucker_decomposition
American mathematician
algorithms with orthogonality constraints, the geometry of the generalized singular value decomposition (GSVD), and applications of Lie algebra to matrix factorizations
Alan_Edelman
Algebraic element satisfying some of the criteria of an inverse
_{1}&0\\0&0\end{bmatrix}}V^{\operatorname {T} }} be its singular-value decomposition. Then for any generalized inverse A g {\displaystyle A^{g}} , there exist
Generalized_inverse
Matrix approximation problem in linear algebra
R^{T}R=I} . To find matrix R {\displaystyle R} , one uses the singular value decomposition (for which the entries of Σ {\displaystyle \Sigma } are non-negative)
Orthogonal_Procrustes_problem
Signal processing technique
the Moore–Penrose inverse, also known as the pseudo-inverse. Singular value decomposition can be employed to compute the pseudo-inverse. If noise is present
Generalized pencil-of-function method
Generalized_pencil-of-function_method
Certain vector fields are the sum of an irrotational and a solenoidal vector field
discussion of Hodge decomposition below. The Hodge decomposition is closely related to the Helmholtz decomposition, generalizing from vector fields on
Helmholtz_decomposition
Statement about integration on manifolds
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called
Generalized_Stokes_theorem
Norm on a vector space of matrices
called "entry-wise" norms. The singular value decomposition is useful in analyzing matrices. A vector norm of the singular values of a matrix may be taken as
Matrix_norm
Mathematical function for the probability a given outcome occurs in an experiment
generate real-valued random variables with any distribution: for be any cumulative distribution function F, let Finv be the generalized left inverse of
Probability_distribution
Vector satisfying some of the criteria of an eigenvector
linearly independent generalized eigenvectors which form a basis for an invariant subspace of V {\displaystyle V} . Using generalized eigenvectors, a set
Generalized_eigenvector
Approximation method in statistics
triangular. A variant of the method of orthogonal decomposition involves singular value decomposition, in which R is diagonalized by further orthogonal
Non-linear_least_squares
Statistical estimation technique
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model. It is used when there
Generalized_least_squares
Matrix with a multiplicative inverse
figure out the transmitted information. Singular matrix Binomial inverse theorem LU decomposition Matrix decomposition Matrix square root Minor (linear algebra)
Invertible_matrix
American mathematician (1932–2007)
1090/S0025-5718-69-99647-1. Golub, G. H.; Reinsch, C. (1971). "Singular Value Decomposition and Least Squares Solutions". Linear Algebra. pp. 134–151. doi:10
Gene_H._Golub
Field of mathematics
between the singular value decomposition and eigenvalue decompositions. This means that most methods for computing the singular value decomposition are similar
Numerical_linear_algebra
Technique in natural language processing
from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the
Latent_semantic_analysis
Area of mathematical analysis
maximal functions, singular integrals, oscillatory integrals, Fourier multipliers, Littlewood–Paley theory, and spectral decompositions. A related tradition
Harmonic_analysis
Construction in functional analysis, useful to solve differential equations
give a decomposition of σ(T). Let h ∈ H and μh be its corresponding spectral measure on σ(T). According to a refinement of Lebesgue's decomposition theorem
Decomposition of spectrum (functional analysis)
Decomposition_of_spectrum_(functional_analysis)
Operation in mathematical calculus
of Daniell for the case of real-valued functions on a set X, generalized by Nicolas Bourbaki to functions with values in a locally compact topological
Integral
South Korean American mathematician
Howland, P.; Park, H. (August 2004). "Generalizing discriminant analysis using the generalized singular value decomposition". IEEE Transactions on Pattern Analysis
Haesun_Park
tridiagonal, generalized real, and generalized real symmetric matrices. In addition, it includes subroutines to perform a singular value decomposition. Originally
EISPACK
Idempotent linear transformation from a vector space to itself
algebra problems: QR decomposition (see Householder transformation and Gram–Schmidt decomposition); Singular value decomposition Reduction to Hessenberg
Projection_(linear_algebra)
Differential operator in mathematics
{\displaystyle S^{N-1}} , often called the spherical Laplacian. This decomposition is the starting point for separation of variables in Laplace's equation
Laplace_operator
Concept in mathematical analysis
0^{+}}\left(2-2{\sqrt {a}}\right)=2.} Sometimes integrals may have two singularities where they are improper. Consider, for example, the function 1/((x +
Improper_integral
Model for representing text documents
as singular value decomposition and lexical databases such as WordNet. Models based on and extending the vector space model include: Generalized vector
Vector_space_model
Method of solving differential equations
space decomposition based on which the smoothing is applied, has to be constructed so that the null space of the singular part of the nearly singular operator
Multigrid_method
Applied mathematics problem
notably Davenport's q-method, QUEST and methods based on the singular value decomposition (SVD). Several methods for solving Wahba's problem are discussed
Wahba's_problem
Generalization of the one-dimensional normal distribution to higher dimensions
{A}}^{\mathrm {T} }} . In the degenerate case where the covariance matrix is singular, the corresponding distribution has no density; see the section below for
Multivariate normal distribution
Multivariate_normal_distribution
Technique in numerical linear algebra
{D}}{\big )}\leq r} has an analytic solution in terms of the singular value decomposition of the data matrix. The result is referred to as the matrix approximation
Low-rank_approximation
Dimension of the column space of a matrix
(LU decomposition) can be unreliable, and a rank-revealing decomposition should be used instead. An effective alternative is the singular value decomposition
Rank_(linear_algebra)
on both sides of the singularity. The forms below normally assume the Cauchy principal value around a singularity in the value of C, but this is not
Lists_of_integrals
Statistics; Vol. 3). — ISBN 978-0125463505. G. M. Fel'dman. On a decomposition of generalized Poisson distributions on groups // Theory of Probability and
Generalized Poisson distribution on a locally compact Abelian group
Generalized_Poisson_distribution_on_a_locally_compact_Abelian_group
Branch of mathematical analysis
{\displaystyle ^{[1]}} The Coimbra derivative can be generalized to any order, leading to the Coimbra Generalized Order Differintegration Operator (GODO) For q
Fractional_calculus
Variable representing a random phenomenon
line is a mixture of discrete part, singular part, and an absolutely continuous part; see Lebesgue's decomposition theorem § Refinement. The discrete part
Random_variable
Matrix that commutes with its conjugate transpose
diagonal values are in general complex and U {\displaystyle U} is a unitary matrix. The left and right singular vectors in the singular value decomposition of
Normal_matrix
(QR, QL, generalized factorizations) EVP – eigenvalue problems SVD – singular value decomposition GEVP – generalized EVP GSVD – generalized SVD Bochkanov
Comparison of linear algebra libraries
Comparison_of_linear_algebra_libraries
Real square matrix whose columns and rows are orthogonal unit vectors
matrix decompositions involve orthogonal matrices, including especially: QR decomposition M = QR, Q orthogonal, R upper triangular Singular value decomposition
Orthogonal_matrix
Mathematical manifold theory
that the Hodge decomposition is a decomposition of cohomology with complex coefficients that usually does not come from a decomposition of cohomology with
Hodge_theory
Linear feedforward neural network model
ISBN 978-0201515602. Gorrell, Genevieve (2006), "Generalized Hebbian Algorithm for Incremental Singular Value Decomposition in Natural Language Processing.", EACL
Generalized_Hebbian_algorithm
Signal processing method
signal subspace that can be computed from the output signals. The singular value decomposition (SVD) of Y {\textstyle \mathbf {Y} } is given as Y = U Σ V †
Estimation of signal parameters via rotational invariance techniques
Estimation_of_signal_parameters_via_rotational_invariance_techniques
Riemannian Penrose inequality Riemannian polyhedron Riemannian singular value decomposition Riemannian submanifold Riemannian submersion Riemannian volume
List of things named after Bernhard Riemann
List_of_things_named_after_Bernhard_Riemann
Relates the homology of two objects to the homology of their product
their product. The classical statement of the Künneth theorem relates the singular homology of two topological spaces X and Y and their product space X ×
Künneth_theorem
Method for finding largest (or smallest) eigenvalues
products. Factorization-free, i.e. does not require any matrix decomposition even for a generalized eigenvalue problem. The costs per iteration and the memory
LOBPCG
Provides integral formulas for all derivatives of a holomorphic function
that for smooth complex-valued functions f {\displaystyle f} of compact support on C {\displaystyle \mathbb {C} } the generalized Cauchy integral formula
Cauchy's_integral_formula
Array of numbers
rows or columns and adding multiples of one row to another row. Singular value decomposition (SVD) expresses any matrix A as a product UDV∗, where U and V
Matrix_(mathematics)
General relativity model near spacetime singularities
other words, the first term of γab decomposition corresponds to H = 0; higher terms are obtained by powers decomposition of matrix H whose components are
BKL_singularity
Concept in geometry
a_{i},b_{i}\rangle } are the singular values of the latter matrix. By the uniqueness of the singular value decomposition, the vectors y ^ i {\displaystyle
Angles_between_flats
Technique in mathematical modeling
for proper orthogonal decomposition, parallel, non-adaptive methods for hyper-reduction, and randomized singular value decomposition. libROM also includes
Model_order_reduction
Algorithm to solve systems of equations
for example, by a singular value decomposition of B {\displaystyle \mathbf {B} } ; a {\displaystyle \mathbf {a} } is a right singular vector of B {\displaystyle
Direct_linear_transformation
Method for estimating the unknown parameters in a linear regression model
{\beta }}} in this case can be interpreted as the coefficients of vector decomposition of ^y = Py along the basis of X. In other words, the gradient equations
Ordinary_least_squares
Multivariate derivative (mathematics)
gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle
Gradient
Statistical method
forecasts of returns and cash-flow growth. A PLS version based on singular value decomposition (SVD) provides a memory efficient implementation that can be
Partial least squares regression
Partial_least_squares_regression
Partial differential equation
Simon Brendle and Richard Schoen. Following the possibility that the singularities of solutions of the Ricci flow could identify the topological data predicted
Ricci_flow
Generalized function whose value is zero everywhere except at zero
distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, where it is infinite
Dirac_delta_function
Matrix of second derivatives
projective curve. The inflection points of the curve are exactly the non-singular points where the Hessian determinant is zero. It follows by Bézout's theorem
Hessian_matrix
Mathematical approximation of a function
{\displaystyle z-a} is known as a Puiseux series. The Taylor series may also be generalized to functions of more than one variable with T ( x 1 , … , x d ) = ∑ n
Taylor_series
Connects homology and cohomology groups for oriented closed manifolds
decomposition. The dual polyhedral decomposition is a cell decomposition of the manifold such that the k-cells of the dual polyhedral decomposition are
Poincaré_duality
Resource problem in machine learning
Reinforcement Learning) algorithm: Similar to LinUCB, but utilizes singular value decomposition rather than ridge regression to obtain an estimate of confidence
Multi-armed_bandit
Principle in geometry and linear algebra
applications to the statistics of principal components analysis and the singular value decomposition. In physics, the theorem is fundamental to the studies of angular
Principal_axis_theorem
Statistical technique
any particular assumptions. The computation of the TLS using singular value decomposition (SVD) is described in standard texts. We can solve the equation
Total_least_squares
In mathematics, invariant of square matrices
methods of solving systems of linear equations, such as LU, QR, or singular value decomposition. Determinants can be used to characterize linearly dependent
Determinant
Way of inferring information from cross-covariance matrices
V=d^{T}\Sigma _{YY}^{-1/2}Y=b^{T}Y} CCA can be computed using singular value decomposition on a correlation matrix. It is available as a function in MATLAB
Canonical_correlation
Estimator for quality of a statistical model
School of Economics Pan, W. (2001), "Akaike's Information Criterion in generalized estimating equations", Biometrics, 57 (1): 120–125, doi:10.1111/j.0006-341X
Akaike_information_criterion
Matrix equal to its conjugate-transpose
Hermitian matrices also appear in techniques like singular value decomposition (SVD) and eigenvalue decomposition. In statistics and machine learning, Hermitian
Hermitian_matrix
Data analysis technique
these notations, computing an MCA consists essentially in the singular value decomposition of the matrix: M = D r − 1 / 2 ( Z − r c T ) D c − 1 / 2 {\displaystyle
Multiple correspondence analysis
Multiple_correspondence_analysis
Java library for linear algebra
thresholding. Algebraic multigrid by smoothed aggregation. Example of Singular Value Decomposition (SVD): SVD svd = new SVD(matA.numRows(),matA.numColumns()); SVD
Matrix_Toolkit_Java
Statistical shape analysis technique
rather than a simple angle, and in this case singular value decomposition can be used to find the optimum value for R (see the solution for the constrained
Procrustes_analysis
Branch of mathematics studying functions of a complex variable
contour integration). A "pole" (or isolated singularity) of a function is a point where the function's value becomes unbounded, or "blows up". If a function
Complex_analysis
Sequence of data points over time
fast variation, and cyclical irregularity: see trend estimation and decomposition of time series Curve fitting is the process of constructing a curve
Time_series
Topological space that locally resembles Euclidean space
schemes Non-singular algebraic varieties over the real or complex numbers are manifolds. One generalizes this first by allowing singularities, secondly
Manifold
Pattern of oscillating motion in a system
non trivial solutions are to be found for those values of ω whereby the matrix on the left is singular; i.e. is not invertible. It follows that the determinant
Normal_mode
distribution Generalized normal distribution Generalized p-value Generalized Pareto distribution Generalized Procrustes analysis Generalized randomized
List_of_statistics_articles
Operation on differential forms
lemma. As suggested by the generalized Stokes' theorem, the exterior derivative is the "dual" of the boundary map on singular simplices. The exterior derivative
Exterior_derivative
Method of evaluating certain integrals along paths in the complex plane
the contour, provided the deformation does not cross a singularity or branch cut. Thus the value of a contour integral between fixed endpoints is not governed
Contour_integration
Iterative method in numerical analysis
which can be solved by standard methods including QR decomposition and singular value decomposition, possibly including regularization techniques to deal
Anderson_acceleration
Visualization method for regularization
criterion has been used for Tikhonov regularization, truncated singular value decomposition and other regularization schemes. It can also be adapted to iterative
L-curve
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
Girl/Female
Muslim/Islamic
Value Worth
Surname or Lastname
English
English : from Middle English sengler, syngler ‘singular’ (Old French se(i)ngler), perhaps a nickname for a solitary person.German : topographic name for a valley dweller, from a diminutive of Middle High German senke ‘valley’ + the suffix -er, denoting an inhabitant.German : habitational name for someone from Singeln near Waldshut.German : variant of Sing 1.
Boy/Male
Muslim
Value, Price
Surname or Lastname
English
English : topographic name for someone who lived in a valley, Middle English vale (Old French val, from Latin vallis). The surname is now also common in Ireland, where it has been Gaelicized as de Bhál.Galician and Aragonese : topographic name from val ‘valley’, or habitational name from any of the places named with this word.
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
Boy/Male
Australian, Finnish
Rule
Boy/Male
Indian
Value, Price
Boy/Male
Arabic
Value
Boy/Male
Gujarati, Hindu, Indian
Value; Inside Trueness
Girl/Female
Arabic, Muslim
Unique; Singular
Boy/Male
Arabic, Muslim
Destiny; Dignity; Value
Girl/Female
Indian
Unique, Singular
Girl/Female
American, British, English, Italian
Of High Value
Girl/Female
Muslim
Unique, Singular
Girl/Female
Arabic
Value; Price
Girl/Female
Celtic
Mythical daughter of Lyr.
Girl/Female
Arabic, Indian, Muslim, Parsi, Sindhi
Value; Price; Worth
Girl/Female
Arabic, Muslim
Superiority; Attribute; Value
Boy/Male
Hindu, Indian
Value
Girl/Female
American, British, English
Of High Value
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
Boy/Male
English
Son of Perkin.
Girl/Female
Hindu, Indian, Marathi
Divine Fortune
Boy/Male
Persian
Wise lord.
Girl/Female
Muslim
Paradise egyptian name
Boy/Male
Arabic, Muslim
Deer-like
Girl/Female
Tamil
Look, Blessed with beauty, Shape, Beauty
Girl/Female
English
Mother.
Girl/Female
Indian
Merciful, Companionate, Kind
Boy/Male
Indian, Sanskrit
With a Variegated Form
Boy/Male
Indian
Signal, Guidance, Guiding hand
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
GENERALIZED SINGULAR-VALUE-DECOMPOSITION
imp. & p. p.
of Value
v. t.
To estimate the value, or worth, of; to rate at a certain price; to appraise; to reckon with respect to number, power, importance, etc.
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
imp. & p. p.
of Generalize
adv.
So as to express one, or the singular number.
v. t.
To be worth; to be equal to in value.
p. pr. & vb. n.
of Generalize
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
n.
The singular number, or the number denoting one person or thing; a word in the singular number.
n.
One who values; an appraiser.
n.
Value.
a.
Distinguished as existing in a very high degree; rarely equaled; eminent; extraordinary; exceptional; as, a man of singular gravity or attainments.
a.
Comprising structural characters which are separated in more specialized forms; synthetic; as, a generalized type.
adv.
Strangely; oddly; as, to behave singularly.
a.
Standing by itself; out of the ordinary course; unusual; uncommon; strange; as, a singular phenomenon.
a.
Each; individual; as, to convey several parcels of land, all and singular.
adv.
In a singular manner; in a manner, or to a degree, not common to others; extraordinarily; as, to be singularly exact in one's statements; singularly considerate of others.
a.
Denoting one person or thing; as, the singular number; -- opposed to dual and plural.
v. i.
Unsettled; unfixed; undetermined; indefinite; ambiguous; as, a vague idea; a vague proposition.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.