Structural Entropic Difference: A Bounded Distance Metric for Unordered Trees

Abstract

We show a new metric for comparing unordered, tree-structured data. While such data is increasingly important in its own right, the methodology underlying the construction of the metric is generic and may be reused for other classes of ordered and partially ordered data. The metric is based on the information content of the two values under consideration, which is measured using Shannon's entropy equations. In essence, the more commonality the values possess, the closer they are. As values in this domain may have no commonality, a good metric should be bounded to represent this. This property has been achieved, but is in tension with triangle inequality.