Global Evaluation for Decision Tree Learning

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.

A note on the triangle inequality for the Jaccard distance

Two simple proofs of the triangle inequality for the Jaccard distance in terms of nonnegative, monotone, submodular functions are given and discussed.