Data Min Knowl Disc DOI 10.1007/s10618-010-0174-x Optimal constraint-based decision tree induction from itemset lattices Siegfried Nijssen · Elisa Fromont Received: 15 April 2009 / Accepted: 6 March 2010 The Author(s) 2010 Abstract In this article we show that there is a strong connection between decision tree learning and local pattern mining. This connection allows us to solve the computationally hard problem of finding optimal decision trees in a wide range of applications by post-processing a set of patterns: we use local patterns to construct a global model. We exploit the connection between constraints in pattern mining and constraints in decision tree induction to develop a framework for categorizing deci- sion tree mining constraints. This framework allows us to determine which model constraints can be pushed deeply into the pattern mining process, and allows us to improve the state-of-the-art of optimal decision tree induction. Keywords Decision tree learning · Formal concepts · Frequent itemset mining · Constraint based mining 1 Introduction Decision trees are among the most popular predictive models and have been studied from many perspectives. However, no general framework exists to constrain the Responsible editor: Johannes Fürnkranz and Arno Knobbe. S. Nijssen (B ) Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium e-mail: Siegfried.Nijssen@cs.kuleuven.be E. Fromont Laboratoire Hubert Curien, CNRS UMR 5516, Université de Saint-Étienne Jean Monnet, Université de Lyon, 42023 Saint-Étienne, France e-mail: Elisa.Fromont@univ-st-etienne.fr 123