Resolving the Sign Ambiguity in the Singular Value Decomposition


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.

Journal of Chemometrics
R. Bro, E. Acar, T. G. Kolda. Resolving the Sign Ambiguity in the Singular Value Decomposition. Journal of Chemometrics, Vol. 22, No. 2, pp. 135-140, 2008.


PCA, sign indeterminacy, SVD, sign flip


author = {Rasmus Bro and Evrim Acar and Tamara G. Kolda}, 
title = {Resolving the Sign Ambiguity in the Singular Value Decomposition}, 
journal = {Journal of Chemometrics}, 
volume = {22}, 
number = {2}, 
pages = {135--140}, 
month = {February}, 
year = {2008},
doi = {10.1002/cem.1122},