About the Normalize operator.

I have a simple question about the Normalize operator.

Suppose this

• I have a dataset (m1 examples, n attributes)
• I normalize them and I get two things: the normalized data and a normalization model.
• To the original data I add m2 new examples.
• To this augmented set of data (m1 + m2 examples) I apply the normalization model obtained previously.

Two things must happen:

1. The new m2 data have been normalized with respect to a model in which they were not present and consequently they do not correspond exactly to what would have been obtained when considering means and variances of the whole set (old plus new)
2. The m1 normalized values from the initial examples must be identical in both results.

Is this correct?

 Thanks!!!!!!!!!!