  We transfer distances on clusterings to the building process of decision
trees, and as a consequence extend the classical ID3 algorithm to perform
modifications based on the global distance of the tree to the ground
truth--instead of considering single leaves. Next, we evaluate this idea in
comparison with the original version and discuss occurring problems, but also
strengths of the global approach. On this basis, we finish by identifying other
scenarios where global evaluations are worthwhile.
