Resolving the sign ambiguity in the singular value decomposition.

Technical Report · Mon Oct 01 00:00:00 EDT 2007

DOI:https://doi.org/10.2172/920802· OSTI ID:920802

Bro, Rasmus ^[1]; Acar, Evrim ^[2]; Kolda, Tamara Gibson

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1. University of Copenhagen, Frederiksberg C, Denmark
2. Rensselaer Polytechnic Institute, Troy, NY

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.

• Research Organization: Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 920802
• Report Number(s): SAND2007-6422; TRN: US200803%%29
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ALGORITHMS
CLASSIFICATION
DATA ANALYSIS
EIGENVALUES
Hypertext systems.
Eigenvalues.
Principal components analysis.