I think it is a matter of juxtaposed terminology and symbols : W^2
designates feature 2, not the Euclidian distance; and W designates
the global cost function (the one that uses all features).
Correct ?
No, feature 2 *is* the Euclidean distance, so W^2 designates both. To be
more specific, W^2 is a matrix of residue-residue Euclidean distances.
There is some scaling done internally so that all the features have
roughly the same magnitude, but that's simply equivalent to changing the
units of distance.
Just to enforce my understanding : What would happen if I set all
features to 0 except for feature 2 ? would the two superpositions be
the same ?
Probably. One would hope that an alignment made using a distance matrix
that is itself extracted from an alignment would reproduce that
alignment, but it's not absolutely guaranteed.