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.
PCA, sign indeterminacy, SVD, sign flip
@article{BrAcKo08,
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},
}