Computational Statistics & Data Analysis 45 (2004) 577–593 www.elsevier.com/locate/csda The comparison between classication trees through proximity measures Rossella Miglio, Gabriele Soritti ∗ Dipartimento di Scienze Statistiche, Universit a degli Studi di Bologna Via delle Belle Arti 41, I-40126 Bologna, Italy Received 14 March 2003; received in revised form 17 March 2003 Abstract Several proximity measures have been proposed to compare classications derived from dier- ent clustering algorithms. There are few proposed solutions for the comparison of two classica- tion trees; some of them measure the dierence between the structures of the trees, some other compare the partitions associated to the trees taking into account their predictive power. Their features and limitations are discussed. Furthermore, a new dissimilarity measure is proposed; it considers both the aspects explored separately by the previous ones. Three of these measures are then compared analyzing two dierent classication problems: a real data set and a simulation study. With respect to the real data set it is also evaluated how and how much each of the considered measures is inuenced by the presence of highly predictive variables which are also highly correlated. c 2003 Elsevier B.V. All rights reserved. Keywords: Classication tree; Proximity measure; Tree topology; Partition 1. Introduction Classication trees represent non-parametric classiers that exploit the local relation- ship between the class variable and the predictors. They allow an automatic feature selection and a hierarchical representation of the measurement space. A typical segmen- tation procedure repeatedly splits the predictor space, generally, in two disjoint regions according to a local optimization criterion; in order to control the eective complexity * Corresponding author. Tel.: +390-5120-98193; fax: +390-5123-2153. E-mail address: soritt@stat.unibo.it (G. Soritti). 0167-9473/$ - see front matter c 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0167-9473(03)00063-X