# Distances between raw and z-scores

1. Jan 3, 2005

### drago

Hi all,
I know how to express the Euclidean distance between two z-normalized vectors using the Pearson correlation coefficient of the raw vectors:

D^2(x_norm, y_norm)=2n(1-corr(x,y))

where the left term is the euclidean distance between the normalized forms and corr is the Pearson correlation coefficient.
The problem is that I would like to express the Euclidean distance beteen the normalized forms as a function of the Euclidena distance of the raw forms:

D^2(x_norm, y_norm) = f(D^2(x,y))

and so far I cannot achieve this.
So, my question is, could someone point me a reference where eventually I could find anything on the topic?

Thank you,
drago