When running PCA it is possible to get at "The number of power iterations is increased to 7 to achieve higher precision." message. I think that might be from #5299?

This is completely useless to a user of PCA that probably didn't even choose the algorithm explicitly.
If the number of power iterations was not provided explicitly, I think there should be no warning. If the user called PCA with the defaults, I don't think there should be a warning.