A singular value decomposition of a \(k\)-way array for a principal component analysis of multiway data, \(\text{PTA-}k\)

DOI10.1016/S0024-3795(97)81516-9zbMath0889.65035WikidataQ59256263 ScholiaQ59256263MaRDI QIDQ1375538

Robert Sabatier, Didier Leibovici

Publication date: 28 January 1998

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

singular value decompositionprincipal component analysislow rank approximationsEckart-Young theoremalternating Gauss-Seidel type iterationmultiindex arrays

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Probabilistic methods, stochastic differential equations (65C99)

Related Items

A randomized algorithm for a tensor-based generalization of the singular value decomposition ⋮ A Constructive Algorithm for Decomposing a Tensor into a Finite Sum of Orthonormal Rank-1 Terms ⋮ On optimal low rank Tucker approximation for tensors: the case for an adjustable core size ⋮ Bounds on strongly orthogonal ranks of tensors ⋮ An inexact augmented Lagrangian method for computing strongly orthogonal decompositions of tensors ⋮ Spline approximation, Kronecker products and multilinear forms ⋮ Numerical Computation for Orthogonal Low-Rank Approximation of Tensors

Cites Work

• The algebra of multimode factor analysis
• Principal component analysis of three-mode data by means of alternating least squares algorithms
• Separation theorems for singular values of matrices and their applications in multivariate analysis
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
• An approach to n-mode components analysis
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Unnamed Item
• Unnamed Item
• Unnamed Item