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Singular Value Decomposition (Read 1980 times)
Gerrit-Jan Linker
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Singular Value Decomposition
06.11.13 at 11:17:53
 
Singular Value Decomposition
 
SVD is based on a theorem from linear algebra which says that any rectangular matrix S can be brought into diagonal form with two unitary matrices U and V.
 
S'=USV
so that S'ij=S'jjδij
 
Singular value decomposition (SVD) can be looked at from three mutually compatible points of view:
  • SVD can be seen as a method for transforming correlated variables into a set of uncorrelated ones that better expose the various relationships among the original data items.  
  • SVD is a method for identifying and ordering the dimensions along which data points exhibit the most variation.  
  • SVD can be seen as a method for data reduction. Once it is identi
    ed where the most variation is, it's possible to  
    find the best approximation of the original data points using fewer dimensions.  

 
Sources:
Ria Broer, INTERNATIONAL    JOURNAL   OF  QUANTUM    CHEMISTRY,   VOL.  45, 587-590   (1993)
http://www.ling.ohio-state.edu/~kbaker/pubs/Singular_Value_Decomposition_Tutoria l.pdf
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« Last Edit: 07.11.13 at 10:54:58 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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