Hi Javier,

We should perform the normalization first then do the PCA. A nice graphical answer is as below:

https://stats.stackexchange.com/questions/69157/why-do-we-need-to-normalize-data-before-analysis

I hope this will help.

Thanks,

Alok

https://stats.stackexchange.com/questions/69157/why-do-we-need-to-normalize-data-before-analysis

It depends on your data type. The rule of thumb is normalise first. But there are situations where it is actually useful to use the PCA scores to normalise your data. However to do it this way you need to understand your data's structure and understand why the rule of thumb works and when it can be ignored.

For an example of when it can be ignored see the papers below. In these papers the data type is very specific. Each variable is a different pixel from a detector so it forms a signal in which the x-axis is stable and the y intensities in each are related through sample identity to all other variables. The range of variance on the Y axis is identical for all variables and is a fixed dynamic range. This bounds the variability and how much it can differ between variables, avoiding the risk of the situation Alok linked to.

See http://onlinelibrary.wiley.com/doi/10.1002/jrs.2896/full (Palacký, Jan, Peter Mojzeš, and Jiří Bok. "SVD‐based method for intensity normalization, background correction and solvent subtraction in Raman spectroscopy exploiting the properties of water stretching vibrations." Journal of Raman Spectroscopy 42.7 (2011): 1528-1539.)

and for a bit of background 

Beattie, J. Renwick, et al. "Effect of signal intensity normalization on the multivariate analysis of spectral data in complex ‘real‐world’datasets." Journal of Raman Spectroscopy 40.4 (2009): 429-435.

According to me as suggested above also normalise first your data and then only go for principal component analysis. That will be best. 

Thanks