A singular value decomposition of a \(k\)-way array for a principal component analysis of multiway data, \(\text{PTA-}k\)
type: Item
instance of: scholarly article
title: A singular value decomposition of a \(k\)-way array for a principal component analysis of multiway data, \(\text{PTA-}k\)
zbMATH Open document ID: 0889.65035
DOI: 10.1016/S0024-3795(97)81516-9
author: Didier Leibovici
author: Robert Sabatier
published in: Linear Algebra and its Applications
publication date: 1998-01-28T00:00:00Z
review text: A generalization of the singular value decomposition to multiindex arrays is studied. It finds a decomposition into a sum of rank one tensors, by first computing the best approximation of the given array by an outer product of vectors, and then recursively decomposing the lower-dimensional arrays obtained by contracting along the vectors of the best approximation. The first step is performed by an alternating Gauss Seidel type iteration. The primary use of this decomposition is to find low rank approximations in the spirit of the Eckart-Young theorem and perform a principal component analysis.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 1100775
zbMATH Keywords: singular value decomposition
zbMATH Keywords: multiindex arrays
zbMATH Keywords: alternating Gauss-Seidel type iteration
zbMATH Keywords: low rank approximations
zbMATH Keywords: Eckart-Young theorem
zbMATH Keywords: principal component analysis
reviewed by: Axel Ruhe
MaRDI profile type: Publication
Wikidata QID: Q59256263
cites work: Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young'' decomposition
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description: scientific article; zbMATH DE number 1100775