Similarity measurement on leaf-labelled trees

We outline a method for measuring in an efficient way an overall degree of similarity between different leaf-labelled trees. In particular, we consider rooted trees, either unordered or ordered and not necessarily carrying the same labels. The trees to be compared are first represented in the form of matrices whose entries are in the interval [O,1] and the actual comparison strategy then relies on a one-parameter class of fuzzy similarity measures that are applied to the matrices. Various tests have been carried out to compare the new method with existing ones and to measure its robustness with regard to varying parameters. feature-space), and the most frequently used similarity measures are the ones based on cardinalities of the sets involved. By far the most popular of these similarity measures is known as Jaccard's coefficient [5], which for given ordinary sets A and B is defined as: Clearly, this similarity measure, which is in terms of strings the ratio between the count of the bits on in both object A and object B and the count of the bits on in objects A or B, is symmetric and reflexive. Another well-known symmetric and reflexive similarity measure is the so-called simple matching coefficient [8], defined as: