Sign correction in SVD and PCA

Determines the right sign of the singular vectors in SVD (score- and loading vectors in PCA)

Description

Although the Singular Value Decomposition (SVD) and eigenvalue decomposition (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. We provide a solution to the sign ambiguity problem by determining the sign of the singular vector from the sign of the inner product of the singular vector and the individual data vectors. The data vectors may have different orientation but it makes intuitive as well as practical sense to choose the direction in which the majority of the vectors point. This can be found by assessing the sign of the sum of the signed inner products.

More info at: R. Bro, E. Acar, and T. G. Kolda. Resolving the sign ambiguity in the singular value decomposition. J.Chemom. 22:135-140, 2008 and at www.models.life.ku.dk

• MATLAB release: MATLAB 7.7 (R2008b)

[Wolfgang]

Hallo,

this is exactly what i was looking for. Sadly i get this message:

??? Cell contents reference from a non-cell array object.

Error in ==> sign_flip at 23
  F(i) = size(loads{i},2);

[Rasmus Bro]

If you look in the help file, you will see that you have to input the 'whole' SVD in order to perform the sign_flip. So you have to do the following

[u,s,v]=svd(X);

loads{1}=u*s;
loads{2}=v;

and then you input loads instead of u. Then it should work.

[Admiral]

Was wondering if you could provide some guidance on how to use this with princomp? Am also trying to get some help on interpreting the results. Any/all info greatly appreciated. Thanks.