Resolving the sign ambiguity in the singular value decomposition.

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Description

Many modern data analysis methods involve computing a matrix singular value decomposition (SVD) or eigenvalue decomposition (EVD). Principal components analysis is the time-honored example, but more recent applications include latent semantic indexing, hypertext induced topic selection (HITS), clustering, classification, etc. Though the SVD and EVD are well-established and can be computed via state-of-the-art algorithms, it is not commonly mentioned that there is an intrinsic sign indeterminacy that can significantly impact the conclusions and interpretations drawn from their results. Here we provide a solution to the sign ambiguity problem and show how it leads to more sensible solutions.

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18 p.

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Bro, Rasmus; Acar, Evrim & Kolda, Tamara Gibson October 2007.

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This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 32 times . More information about this report can be viewed below.

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Description

Many modern data analysis methods involve computing a matrix singular value decomposition (SVD) or eigenvalue decomposition (EVD). Principal components analysis is the time-honored example, but more recent applications include latent semantic indexing, hypertext induced topic selection (HITS), clustering, classification, etc. Though the SVD and EVD are well-established and can be computed via state-of-the-art algorithms, it is not commonly mentioned that there is an intrinsic sign indeterminacy that can significantly impact the conclusions and interpretations drawn from their results. Here we provide a solution to the sign ambiguity problem and show how it leads to more sensible solutions.

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18 p.

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  • Report No.: SAND2007-6422
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/920802 | External Link
  • Office of Scientific & Technical Information Report Number: 920802
  • Archival Resource Key: ark:/67531/metadc900575

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Office of Scientific & Technical Information Technical Reports

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  • October 2007

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

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  • Feb. 22, 2018, 8:17 p.m.

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Bro, Rasmus; Acar, Evrim & Kolda, Tamara Gibson. Resolving the sign ambiguity in the singular value decomposition., report, October 2007; United States. (digital.library.unt.edu/ark:/67531/metadc900575/: accessed September 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.