Hypervector Analysis of the Voynich Manuscript

[Alin_J]

In the (hypothetical) case that Darrin omitted that mapping, then the plots should come out looking the same, but the scales for the two axes would be different.

Any linear scaling of the original data will only change the scaling of the principal components in the end result of PCA, true. But still, during PCA component calculation, all the data must be translated/centered around 0 (mean-subtracted) to work because it's based on variance and co-variance in the data and these are used to calculate the directions of correlation in the data. This is why the routines for PCA in software automatically does it for you so you don't have to think about it.

So, it doesn't matter how much you scale or translate the data before this, as long as you do the same for all the data, but internally, this step is still critical to ensure that PCA gives the correct result.

Variances and co-variances are products and squares of the mean-centered deviations, so they will not increase proportionally/linearly with the deviation. This means that if a mean-centering should not have been performed either by the software during PCA or by you it will show false results and correlations with e.g. the principal components rotated more in relationship with the original vectors in wrong directions.