Mining First-Order Temporal Interval Patterns with Regular Expression Constraints ⋆ Sandra de Amo 1 , Arnaud Giacometti 2 , and Waldecir Pereira Junior 1 1 Universidade Federal de Uberlˆandia, Faculdade de Computa¸c˜ao, Av. Jo˜ao Naves de Avila, 2121, Bloco B, Uberlˆandia-MG, Brazil, deamo@ufu.br, wpjunior@gmail.com 2 Universit´ e de Tours, Laboratoire d’Informatique, 3, Place Jean Jaur` es 45000 Blois, France, giaco@univ-tours.fr Abstract. Most methods for temporal pattern mining assume that time is represented by points in a straight line starting at some initial instant. In this paper, we consider a new kind of first order temporal pattern, specified in Allen’s Temporal Interval Logic, where time is explicitly rep- resented by intervals. We present the algorithm MILPRIT for mining temporal interval patterns, which uses variants of the classical level-wise search algorithms. MILPRIT allows a broad spectrum of constraints over temporal patterns to be incorporated in the mining process. Some ex- perimental results over synthetic and real data are presented. Key words: Temporal Data Mining, First-Order Temporal Interval Logic, Constraint-based Mining, Sequential Patterns. 1 Introduction We present a new sequential pattern where time is mesured in terms of intervals instead of points. These patterns, which we call temporal interval patterns, aim at capturing how events taking place in time intervals relate to each other. For instance, (1) in a medical application, we could be interested in discovering if patients who take some medicine X during a certain period of time, and who presented the symptom Y before taking the medicine, will present the symptom Z during or after taking the medicine X, (2) in an agricultural application, we could be interested in discovering if the use of some organic fertilizer during a period of time has an effect on the way a plant grows during and after the fertilizer application. In [6], Allen’s Propositional Interval Logic [3] has been used for the first time, to treat the problem of discovering association rules over time series. However, to our knowledge the use of Interval Logic in temporal data mining has been restricted to propositional temporal patterns, that is, patterns not involving first order predicates. The need for more expressive kind of temporal patterns arises for instance, when modelling Unix-users behaviour [7], as is pointed out in [8]. Our temporal pattern is defined as a set of atomic first order formulae where time is explicitly represented by an interval variable, together with a set of interval relationships (before,during,starts,finishes,overlaps,meets ) described in ⋆ Research partially supported by CNPq-Brazil, project no. 473309/2004-1.