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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
Name of two different techniques based on the singular value decomposition
the generalized singular value decomposition (GSVD) is the name of two different techniques based on the singular value decomposition (SVD). The two versions
Generalized singular value decomposition
Generalized_singular_value_decomposition
Square roots of the eigenvalues of the self-adjoint operator
rectangular diagonal matrix with the singular values lying on the diagonal. This is the singular value decomposition. For A ∈ C m × n {\displaystyle A\in
Singular_value
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
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
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
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
Generalized matrix decomposition for Lie groups and Lie algebras
and representation theory. It generalizes the polar decomposition or singular value decomposition of matrices. Its history can be traced to the 1880s
Cartan_decomposition
Nonparametric spectral estimation method
interpretation. The name "singular spectrum analysis" relates to the spectrum of eigenvalues in a singular value decomposition of a covariance matrix, and
Singular_spectrum_analysis
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
Regularization technique for ill-posed problems
the singular-value decomposition. Given the singular value decomposition A = U Σ V T {\displaystyle A=U\Sigma V^{\mathsf {T}}} with singular values σ i
Ridge_regression
Tensor decomposition
generalized to higher mode analysis, which is also called higher-order singular value decomposition (HOSVD) or the M-mode SVD. The algorithm to which the literature
Tucker_decomposition
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
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
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
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
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
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
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
Square matrix without an inverse
exploit SVD: singular value decomposition yields low-rank approximations of data, effectively treating the data covariance as singular by discarding
Singular_matrix
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)
Process in linear algebra
unique up to re-ordering. The Schmidt decomposition is essentially a restatement of the singular value decomposition in a different context. Fix orthonormal
Schmidt_decomposition
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
Method for finding largest (or smallest) eigenvalues
be trivially adapted for computing several largest singular values and the corresponding singular vectors (partial SVD), e.g., for iterative computation
LOBPCG
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
transformations can be decomposed in a way that resembles Singular Value Decomposition, but which also unifies it with the Jordan decomposition. We therefore have
Laguerre_transformations
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
Methods for numerical approximations
decompositions or singular value decompositions. For instance, the spectral image compression algorithm is based on the singular value decomposition.
Numerical_analysis
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
More equations than unknowns (mathematics)
right-triangular system R x = Q T b . {\displaystyle Rx=Q^{T}b.} The Singular Value Decomposition (SVD) of a (tall) matrix A {\displaystyle A} is the representation
Overdetermined_system
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
Concept in linear algebra
matrix decomposition algorithm based on the QR factorization which can be used to determine the rank of a matrix. The singular value decomposition can be
RRQR_factorization
Concept in linear algebra
construct a full-rank factorization of A {\textstyle A} via a singular value decomposition A = U Σ V ∗ = [ U 1 U 2 ] [ Σ r 0 0 0 ] [ V 1 ∗ V 2 ∗ ] = U 1
Rank_factorization
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
Algorithms for matrix decomposition
rank, new components can be discovered using the generalized singular value decomposition. To decrease the rank, pairs of components may be greedily merged
Non-negative matrix factorization
Non-negative_matrix_factorization
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
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
Matrix decomposition Cholesky decomposition LU decomposition QR decomposition Polar decomposition Reducing subspace Spectral theorem Singular value decomposition
Outline_of_linear_algebra
Graphical representation of the ease with which a robotic arm can move its end effector
configuration. The axis of the ellipsoid can be computed by using the singular value decomposition of the robot Jacobian. Spong, M.W.; Hutchinson, Seth; Vidyasagar
Manipulability_ellipsoid
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
Numerical algorithm for mortality forecasting
mortality rates in the same format as the input. The model uses singular value decomposition (SVD) to find: A univariate time series vector k t {\displaystyle
Lee–Carter_model
Artificial intelligence project
learning algorithms. One representation, called AnalogySpace, uses singular value decomposition to generalize and represent patterns in the knowledge in ConceptNet
Open_Mind_Common_Sense
Concepts from linear algebra
orthogonal decomposition of a PSD matrix is used in multivariate analysis, where the sample covariance matrices are PSD. This orthogonal decomposition is called
Eigenvalues_and_eigenvectors
JAMA are: Eigensystem solving LU decomposition Singular value decomposition QR decomposition Cholesky decomposition Versions exist for both C++ and the
JAMA (numerical linear algebra library)
JAMA_(numerical_linear_algebra_library)
Dimensionality reduction algorithm
Eigenvalue decomposition Empirical mode decomposition Global mode Normal mode Proper orthogonal decomposition Singular-value decomposition Schmid, Peter
Dynamic_mode_decomposition
be used in the same way as the low-rank approximation of the singular value decomposition (SVD). CUR approximations are less accurate than the SVD, but
CUR_matrix_approximation
the singular value decomposition (SVD). However, it is computed within finite operations, while SVD requires iterative schemes to find singular values. The
Bidiagonalization
eigenvalues. SVD contains solvers for the singular value decomposition as well as the generalized singular value decomposition. Solvers based on the cross-product
SLEPc
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
frequencies ω = ω i {\displaystyle \omega =\omega _{i}} . Do a singular value decomposition of the power spectral density, i.e. G ^ y y ( j ω i ) = U i S
Frequency domain decomposition
Frequency_domain_decomposition
Method for approximating eigenvalues
left and right singular vectors of the original matrix M {\displaystyle M} representing an approximate Truncated singular value decomposition (SVD) with left
Rayleigh–Ritz_method
Physicist and geneticist
Orly; Brown, Patrick O.; Botstein, David (29 August 2000). "Singular value decomposition for genome-wide expression data processing and modeling". Proceedings
Orly_Alter
Use of a DecompositionFactory to compute a Singular Value Decomposition with a Dense Double Row Major matrix (DDRM): SingularValueDecomposition_F64<DenseMatrix64F>
Efficient_Java_Matrix_Library
Software library for numerical linear algebra
equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix
LAPACK
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
Square matrix in which each ascending skew-diagonal from left to right is constant
2-norm) to measure the error of our approximation. This suggests singular value decomposition as a possible technique to approximate the action of the operator
Hankel_matrix
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
algebra, the complete orthogonal decomposition is a matrix decomposition. It is similar to the singular value decomposition, but typically somewhat cheaper
Complete orthogonal decomposition
Complete_orthogonal_decomposition
Distribution of singular values of large rectangular random matrices
distribution, or Marchenko–Pastur law, describes the asymptotic behavior of singular values of large rectangular random matrices. The theorem is named after Soviet
Marchenko–Pastur_distribution
Lagrange multipliers has been introduced by Agmon et al. Recently, singular value decomposition and principal component analysis of the surprisal was utilized
Surprisal_analysis
matrices. In addition, it includes subroutines to perform a singular value decomposition. Originally written around 1972–1973, EISPACK, like LINPACK and
EISPACK
Projection of data onto lower-dimensional manifolds
as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
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
Neural network that learns efficient data encoding in an unsupervised manner
the principal components may be recovered from them using the singular value decomposition. However, the potential of autoencoders resides in their non-linearity
Autoencoder
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
Numerical method that reduces the complexity of computationally intensive simulations
component analysis from Pearson in the field of statistics, or the singular value decomposition in linear algebra because it refers to eigenvalues and eigenvectors
Proper orthogonal decomposition
Proper_orthogonal_decomposition
Dictionary learning algorithm
for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering
K-SVD
important class of modern invariants methods is based on the use of singular value decomposition (SVD) to examine the rank of matrices corresponding to flattenings
Phylogenetic_invariants
used by LAPACK. Higher level algorithms, such as LU decomposition and singular value decomposition, are provided by JAMA, also developed at NIST, which
Template_Numerical_Toolkit
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
Method for analyzing semantic data
tables (usually via a singular value decomposition), probabilistic latent semantic analysis is based on a mixture decomposition derived from a latent
Probabilistic latent semantic analysis
Probabilistic_latent_semantic_analysis
Topics referred to by the same term
International Airport (IATA airport code SVD) on Saint Vincent island Singular value decomposition of a matrix in mathematics Svenska Dagbladet (SvD), a Swedish
SVD
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
semi-definite, then the singular values and eigenvalues of A {\displaystyle A} coincide. In this case, if the singular value decomposition (SVD) is available
Pseudo-determinant
solved as R is upper triangular. An alternative decomposition of X is the singular value decomposition (SVD) X = U Σ V T {\displaystyle X=U\Sigma V^{\rm
Numerical methods for linear least squares
Numerical_methods_for_linear_least_squares
Vector operation
application of the Singular Value Decomposition (SVD) (and Spectral Decomposition as a special case). In particular, the decomposition can be interpreted
Outer_product
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
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
Mathematical procedure
item is referred to as latent factors. Note that, in Funk MF no singular value decomposition is applied, it is a SVD-like machine learning model. The predicted
Matrix factorization (recommender systems)
Matrix_factorization_(recommender_systems)
Algorithm used by recommender systems
networks, clustering models, latent semantic models such as singular value decomposition, probabilistic latent semantic analysis, multiple multiplicative
Collaborative_filtering
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
Computing joint values of a kinematic chain from a known end position
reasonably small positive value. Taking the Moore–Penrose pseudoinverse of the Jacobian (computable using a singular value decomposition) and re-arranging terms
Inverse_kinematics
Vector quantization algorithm minimizing the sum of squared deviations
Vinay, Vishwanathan (2004). "Clustering large graphs via the singular value decomposition" (PDF). Machine Learning. 56 (1–3): 9–33. Bibcode:2004MLear.
K-means_clustering
Type of algorithm
accounted for (for example, the case of H not having an inverse). If singular value decomposition (SVD) routines are available the optimal rotation, R, can be
Kabsch_algorithm
Process of reducing the number of random variables under consideration
mapping Semantic mapping (statistics) Semidefinite embedding Singular value decomposition Sufficient dimension reduction Topological data analysis Weighted
Dimensionality_reduction
Type of continuous linear operator
space need not be self-adjoint or normal. Nevertheless, it has a singular-value decomposition. If T : H 1 → H 2 {\displaystyle T:H_{1}\to H_{2}} is compact
Compact_operator
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
Algebraic object with geometric applications
Lieven; De Moor, Bart; Vandewalle, Joos (2000). "A Multilinear Singular Value Decomposition" (PDF). SIAM J. Matrix Anal. Appl. 21 (4): 1253–1278. doi:10
Tensor
Term in quantum mechanics
the (always real and non-negative) singular values of A {\displaystyle A} , as in the singular value decomposition. The inequality is saturated and becomes
Fidelity_of_quantum_states
Theorem of matrix ranks
approximated by a low-rank matrix UCV, for example using the singular value decomposition. This is applied, e.g., in the Kalman filter and recursive least
Woodbury_matrix_identity
Mathematical concept
This decomposition is closely related to the singular value decomposition of a matrix and is known as an 'Euler' or 'Bloch-Messiah' decomposition. The
Symplectic_matrix
Matrix of inner products of vectors
the Gram matrix is the singular value decomposition. The Gram matrix is symmetric in the case the inner product is real-valued; it is Hermitian in the
Gram_matrix
Techniques for lossy compression of neural networks
{\displaystyle W} . Low-rank approximations can be found by singular value decomposition (SVD). The choice of rank for each weight matrix is a hyperparameter
Model_compression
Approach to dimensionality reduction
the higher-order singular value decomposition (HOSVD) to subspace learning. Hence, its origin is traced back to the Tucker decomposition in 1960s. A TVP
Multilinear_subspace_learning
Italian mathematician (1835–1900)
sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several
Eugenio_Beltrami
System to predict users' preferences
text analysis models, including latent semantic analysis (LSA), singular value decomposition (SVD), latent Dirichlet allocation (LDA), etc. Their uses have
Recommender_system
Filling in missing entries of a matrix
observed entry per row and column of M {\displaystyle M} . The singular value decomposition of M {\displaystyle M} is given by U Σ V † {\displaystyle U\Sigma
Matrix_completion
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)
SINGULAR VALUE-DECOMPOSITION
SINGULAR VALUE-DECOMPOSITION
Girl/Female
American, British, English, Italian
Of High Value
Girl/Female
Indian
Unique, Singular
Girl/Female
Arabic, Muslim
Superiority; Attribute; Value
Boy/Male
Gujarati, Hindu, Indian
Value; Inside Trueness
Girl/Female
American, British, English
Of High Value
Boy/Male
Arabic, Muslim
Destiny; Dignity; Value
Boy/Male
Hindu, Indian
Value
Girl/Female
Muslim/Islamic
Value Worth
Boy/Male
Anglo, British, English, Finnish, Swedish
Valley; Usually with a Stream; From the Glen
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
Australian, Finnish
Rule
Girl/Female
Celtic
Mythical daughter of Lyr.
Girl/Female
Arabic, Muslim
Unique; Singular
Girl/Female
Arabic, Indian, Muslim, Parsi, Sindhi
Value; Price; Worth
Boy/Male
Indian
Value, Price
Girl/Female
Muslim
Unique, Singular
Boy/Male
Muslim
Value, Price
Boy/Male
Arabic
Value
Girl/Female
Arabic
Value; Price
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.
SINGULAR VALUE-DECOMPOSITION
SINGULAR VALUE-DECOMPOSITION
Girl/Female
Indian
Name of a mountain in Medina, Contentment
Girl/Female
Indian, Punjabi, Sikh
The Brave Soldier
Girl/Female
Arabic, German, Gujarati, Hindu, Indian, Kannada, Malayalam, Muslim, Parsi, Tamil, Turkish, Zoroastrian
Princess; Lady; Flute; Instrument Played by Lord Krishna; Suns; Sun
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Jewel in the Crown
Male
Gaelic
Gaelic form of French Bernard, BEARNARD means "bold as a bear."
Surname or Lastname
English
English : unexplained.
Boy/Male
Tamil
Shithikantan | ஷிதீகாஂதந
Lord Shiva
Girl/Female
Tamil
Safety, Security, Welfare, Tranquility, Goddess Durga
Surname or Lastname
English
English : nickname from Middle English, Old French grace ‘charm’, ‘pleasantness’ (Latin gratia).English : from the female personal name Grace, which was popular in the Middle Ages. This seems in the first instance to have been from a Germanic element grīs ‘gray’ (see Grice 1), but was soon associated by folk etymology with the Latin word meaning ‘charm’.
Surname or Lastname
English
English : variant of Garrett 2.
SINGULAR VALUE-DECOMPOSITION
SINGULAR VALUE-DECOMPOSITION
SINGULAR VALUE-DECOMPOSITION
SINGULAR VALUE-DECOMPOSITION
SINGULAR VALUE-DECOMPOSITION
adv.
So as to express one, or the singular number.
n.
Value.
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.
v. t.
To raise to estimation; to cause to have value, either real or apparent; to enhance in value.
a.
Each; individual; as, to convey several parcels of land, all and singular.
a.
Denoting one person or thing; as, the singular number; -- opposed to dual and plural.
a.
Standing by itself; out of the ordinary course; unusual; uncommon; strange; as, a singular phenomenon.
n.
Precise signification; import; as, the value of a word; the value of a legal instrument
a.
Distinguished as existing in a very high degree; rarely equaled; eminent; extraordinary; exceptional; as, a man of singular gravity or attainments.
n.
One who values; an appraiser.
v. i.
Unsettled; unfixed; undetermined; indefinite; ambiguous; as, a vague idea; a vague proposition.
n.
The singular number, or the number denoting one person or thing; a word in the singular number.
n.
The relative length or duration of a tone or note, answering to quantity in prosody; thus, a quarter note [/] has the value of two eighth notes [/].
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.
a.
Highly regarded; esteemed; prized; as, a valued contributor; a valued friend.
v. t.
To rate highly; to have in high esteem; to hold in respect and estimation; to appreciate; to prize; as, to value one for his works or his virtues.
v. t.
To be worth; to be equal to in value.
adv.
Strangely; oddly; as, to behave singularly.
a.
Measured by an angle; as, angular distance.