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Multilinear extension of principal component analysis
Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA) that is used to analyze M-way arrays,
Multilinear principal component analysis
Multilinear_principal_component_analysis
Method of data analysis
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data
Principal_component_analysis
Approach to dimensionality reduction
Multilinear subspace learning algorithms are higher-order generalizations of linear subspace learning methods such as principal component analysis (PCA)
Multilinear_subspace_learning
Study of locomotion
Edition Gait Abnormality Rating Scale Gait deviations Multilinear principal component analysis Multilinear subspace learning Pattern recognition Terrestrial
Gait_analysis
Overview of and topical guide to machine learning
Multidimensional analysis Multifactor dimensionality reduction Multilinear principal component analysis Multiple correspondence analysis Multiple discriminant
Outline_of_machine_learning
Automated recognition of patterns and regularities in data
experts Bayesian networks Markov random fields Unsupervised: Multilinear principal component analysis (MPCA) Kalman filters Particle filters Gaussian process
Pattern_recognition
Matrix decomposition
decomposition Multilinear principal component analysis (MPCA) Nearest neighbor search Non-linear iterative partial least squares Polar decomposition Principal component
Singular_value_decomposition
Process of reducing the number of random variables under consideration
reduction through multilinear subspace learning. The main linear technique for dimensionality reduction, principal component analysis, performs a linear
Dimensionality_reduction
Prevalence Principal component analysis Multilinear principal-component analysis Principal component regression Principal geodesic analysis Principal stratification
List_of_statistics_articles
Algebraic object with geometric applications
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space
Tensor
Class of mathematical software
software: Multilinear principal component analysis. UMPCA Multilinear subspace learning software: Uncorrelated multilinear principal component analysis. UMLDA
Tensor_software
Topics referred to by the same term
Corporation of America, an American film production company Multilinear principal component analysis, a mathematical procedure This disambiguation page lists
MPCA
Branch of mathematics
light waves, seismic waves, and even images, Fourier analysis can isolate individual components of a compound waveform, concentrating them for easier
Mathematical_analysis
Tensor decomposition
decomposition Multilinear principal component analysis Ledyard R. Tucker (September 1966). "Some mathematical notes on three-mode factor analysis". Psychometrika
Tucker_decomposition
Spatial statistical signal analysis
term is also interchangeable with the geographically weighted Principal components analysis in geophysics. The i th basis function is chosen to be orthogonal
Empirical orthogonal functions
Empirical_orthogonal_functions
Approach of analyzing data sets in statistics
Dimensionality reduction: Multidimensional scaling Principal component analysis (PCA) Multilinear PCA Nonlinear dimensionality reduction (NLDR) Iconography
Exploratory_data_analysis
Study of vector bundles, principal bundles, and fibre bundles
bundles or principal bundles, or involving sections of vector bundles, and so there are strong links between gauge theory and geometric analysis. These equations
Gauge_theory_(mathematics)
Representation of mechanical stress at every point within a deformed 3D object
{n} }} . The three stresses normal to these principal planes are called principal stresses. The components σ i j {\displaystyle \sigma _{ij}} of the stress
Cauchy_stress_tensor
Branch of mathematics
manifolds. It uses the techniques of vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry
Differential_geometry
Geometrical concept relating area and volume
partitioning the interior of a triangular prism into three pyramidal components of equal volumes. One may show the equality of those three volumes by
Cavalieri's_principle
Family of distributions that generalize the multivariate normal distribution
models (especially for the growth curve model). The analysis of multivariate models uses multilinear algebra (particularly Kronecker products and vectorization)
Elliptical_distribution
Algebra based on a vector space with a quadratic form
e_{4}^{2}=0.} The general element of the Clifford algebra Cl(R4, d) has 16 components. The linear combination of the even degree elements defines the even subalgebra
Clifford_algebra
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is
Moment_of_inertia
Branch of mathematics
over a field. For more details, see Linear equation over a ring. In multilinear algebra, one considers multivariable linear transformations, that is
Linear_algebra
Subset of artificial intelligence
provided during training. Classic examples include principal component analysis and cluster analysis. Feature learning algorithms, also called representation
Machine_learning
Branch of applied mathematics
of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions, with an Account of the Principal Transcendental
Mathematical_physics
Algorithms for matrix decomposition
"The Multilinear Engine: A Table-Driven, Least Squares Program for Solving Multilinear Problems, including the n-Way Parallel Factor Analysis Model"
Non-negative matrix factorization
Non-negative_matrix_factorization
Physical theory with fields invariant under the action of local "gauge" Lie groups
there is a principal bundle P whose base space is space or spacetime and structure group is a Lie group, then the sections of P form a principal homogeneous
Gauge_theory
Difficulties arising when analyzing data with many aspects ("dimensions")
Linear least squares Model order reduction Multilinear PCA Multilinear subspace learning Principal component analysis Singular value decomposition Bellman,
Curse_of_dimensionality
Array of numbers
multiplication of a two-component vector with a two-by-two matrix called ray transfer matrix analysis: the vector's components are the light ray's slope
Matrix_(mathematics)
Functions in harmonic analysis mathematics
Coifman, Ronald; Meyer, Yves (1997), Wavelets: Calderón-Zygmund and multilinear operators, Cambridge Studies in Advanced Mathematics, vol. 48, Cambridge
Singular_integral
Specification of a derivative along a tangent vector of a manifold
be a tensor field of type (p, q). Consider T to be a differentiable multilinear map of smooth sections α1, α2, ..., αq of the cotangent bundle T∗M and
Covariant_derivative
software product designed for manipulation of mathematical formulae. The principal objective of a computer algebra system is to systematize monotonous and
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
reduction Sliced inverse regression Principal component analysis Linear discriminant analysis Curse of dimensionality Multilinear subspace learning Cook & Adragni
Sufficient dimension reduction
Sufficient_dimension_reduction
Norm on a vector space of matrices
norms". Linear and Multilinear Algebra. 13 (2): 97–99. doi:10.1080/03081088308817508. ISSN 0308-1087. Horn, Roger A. (2012). Matrix analysis. Johnson, Charles
Matrix_norm
Physical quantities taking values at each point in space and time
specifying its value at a point in spacetime requires three numbers, the components of the gravitational field vector at that point. Moreover, within each
Field_(physics)
Expression that may be integrated over a region
universal property of exterior powers, this is equivalently an alternating multilinear map: β p : ⨁ n = 1 k T p M → R . {\displaystyle \beta _{p}\colon \bigoplus
Differential_form
Math/physics concept
formulated subsequent to Cartan's initial work. In particular, on a principal bundle, a principal connection is a natural reinterpretation of the connection form
Connection_form
Tensor invariant under permutations of vectors it acts on
Springer-Verlag, ISBN 3-540-19375-8. Greub, Werner Hildbert (1967), Multilinear algebra, Die Grundlehren der Mathematischen Wissenschaften, Band 136
Symmetric_tensor
Theorem in linear algebra
780-783. Friedland, S., 1981. Convex spectral functions. Linear and multilinear algebra, 9(4), pp.299-316. Miroslav Fiedler; Charles R. Johnson; Thomas
Perron–Frobenius_theorem
Algorithmic technique using hashing
invented in 2008 Multilinear subspace learning – Approach to dimensionality reduction Principal component analysis – Method of data analysis Random indexing
Locality-sensitive_hashing
Technology capable of matching a face from an image against a database of faces
contains other objects gained traction in the early 1990s with the principal component analysis (PCA). The PCA method of face detection is also known as Eigenface
Facial_recognition_system
Theory of subatomic structure
non-symmetric metric tensor, while much later Brans and Dicke added a scalar component to gravity. These ideas would be revived within string theory, where they
String_theory
Tensor in differential geometry
for each point p ∈ M {\displaystyle p\in M} , it gives rise to a (multilinear) map: R p : T p M × T p M × T p M → T p M . {\displaystyle \operatorname
Ricci_curvature
Numerical methods for matrix eigenvalue calculation
(1993). "On the eigenvalues of principal submatrices of normal, hermitian and symmetric matrices". Linear and Multilinear Algebra. 36 (1): 69–78. doi:10
Eigenvalue_algorithm
Type of derivative in differential geometry
define a vector field X over the principal bundle such that its horizontal component matches Y and its vertical component agrees with the connection. This
Lie_derivative
Construct in differenital geometry
connection for which the covariant derivatives of the metric on E vanish. A principal connection on the bundle of orthonormal frames of E. A special case of
Metric_connection
Intrinsic geometric structures in mathematics
p-forms can be identified with the space of alternating p-fold C∞(F)-multilinear maps on the module of vector fields. For further details see Helgason
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Representation of a matrix as a product
Stewart (2011). Matrix splitting Non-negative matrix factorization Principal component analysis If a non-square matrix is used, however, then the matrix U will
Matrix_decomposition
Manifold upon which it is possible to perform calculus
bundle. Each element of the bundle is a tensor field, which can act as a multilinear operator on vector fields, or on other tensor fields. The tensor bundle
Differentiable_manifold
Theory of interwoven space and time by Albert Einstein
constitutes a timelike component ct and spacelike component x = (x, y, z), in a contravariant position four-vector with components: X ν = ( X 0 , X 1 ,
Special_relativity
Electromagnetism in general relativity
distinguishing between free and bound electric charges may facilitate analysis. When the distinction is made, they are called the macroscopic Maxwell's
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Construct allowing differentiation of tangent vector fields of manifolds
principal GL(n)-connection on FM. The 1-forms arising in the flat model are just the components of θ and ω. An affine connection on M is a principal Aff(n)-bundle
Affine_connection
Topics referred to by the same term
containing sub-linear Semilinear (disambiguation) Bilinear (disambiguation) Multilinear (disambiguation) Piecewise linear (disambiguation) Quasilinear (disambiguation)
Linear_(disambiguation)
Mathematics of smooth surfaces
correspond to the principal curvatures of the surface and the eigenvectors are the corresponding principal directions. The principal directions specify
Differential geometry of surfaces
Differential_geometry_of_surfaces
Study of curves from a differential point of view
\mathbb {R} ^{n}} that is r-times continuously differentiable (that is, the component functions of γ are r-times continuously differentiable), where n ∈ N {\displaystyle
Differentiable_curve
Object in differential geometry
while the covariant derivative is only defined for vector fields. The components of the torsion tensor T c a b {\displaystyle T^{c}{}_{ab}} in terms of
Torsion_tensor
Computer hardware and software capable of playing chess
Programs, Seattle, Washington, August 18, 2006 Stiller, Lewis (1996), Multilinear Algebra and Chess Endgames (PDF), Berkeley, California: Mathematical
Computer_chess
Structure defining distance on a manifold
(covariant) components of a covector a[f] the (contravariant) components of a vector v[f] given is called raising the index. In components, (9) is v i
Metric_tensor
Sub-theory of Chinese Marxist thought
notion in historical materialism that history was unilinear rather than multilinear, and proved that other factors than the productive forces in society
Primary_stage_of_socialism
Non-tensorial representation of the spin group
familiar two component spinors used in non relativistic quantum mechanics. Likewise using the 4 × 4 Dirac gamma matrices gives rise to the 4 component Dirac
Spinor
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