We have found several problems in the implementation of the method to automatically tune the number of components of the PCA algorithms:

1. The algorithm never tests full rank: this is most probably due to the fact that loops using the rank end always at rank-1 (for i in range(rank)).
2. If two eigen values are equals there is a log(0) issue.
3. Zeros eigen values are not treated explicitly

Possible solutions:

• For (1): Checking the loops ranges
• For (3): Predetecting small eigen values lower than the numerical noise excluding them from rank scan

I have no idea for 2. We had the problem here with very small eigen values (in numerical noise) which were totally identical. I never managed to create a syntetic dataset which reproduce the problem since the even with symetric datasets, there is always a small difference (in the order of numerical precision) between theoretically identical eigen values.