Proximity measures between classification trees

Several proximity measures have been proposed to compare classifications derived from different clustering algorithms. Few are the proposed solutions for the comparison of two classification trees. We have considered particularly two of these: one (Shannon and Banks, 1999) is a distance that measures the amount of rearrangement needed to change one of the trees so that they result in an identical structure, while the other (Miglio, 1996) is a similarity measure that compares the partitions associated to the trees taking into account their predictive power. In this paper we analyze features and limitations of these proximity measures and suggest a normalizing factor for the distance defined by Shannon and Banks; furthermore we propose a new dissimilarity measure that considers both the aspects explored separately by the previous ones.