I am applying PCA on my data (Image sequences) but got different results when I used the PCA (Matlab Toolbox) command and doing it manually makind matrix and using SVD command.
After doing some search I found that matlab enforces some sign conventions in the PCA code on coefficients calculation, Why is that?
As mentioned in this article is for sign ambiguity problem.
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.