Optimal Multiple Intervals Discretization of Continuous Attributes for Supervised Learning

5, av Pierre Mend&s-France 69676 BRON CEDEX FRANCE {zighed,rakotoma,ffeschet)@univ-lyon2.fr In this paper, we propose an extension of Fischer’s algorithm to compute the optimal discretization of a continuous variable in the context of supervised learning. Our algorithm is extremely performant since its only depends on the number of runs and not directly on the number of points of the sample data set. We propose an empirical comparison between the optimal algorithm and two hill climbing heuristics. In the next section, we present a formulation of the problem of discretization, then we describe an extension of Lechevallier’s algorithm to find the optimal discretisation and we insist on the use of runs instead of the points of the sample data set. After, we introduce two hill-climbing strategies. Finaly, we present experiments and empirical studies of the performances of the various presented stategies. Introduction Formulation Rule induction from examples, such as the well known induction trees (Breiman et al. 1984)) usually use categorial variables. Hence, to manipulate continuous variables, it is necessary to transform them to be compatible with the learning strategy. The processus of splitting the continuous domain of an attribute into a set of disjoints intervals is called discretization. In this paper, we focus on supervised learning where we take into account a class Y(.) to predict. Let be Dx the domain of definition of a continuous attribute X( .). The discretization of X( .) consist in splitting DX into k intervals 1j, j = 1,. . . , k with k 2 1. We note Ij = [dj-1, dj [ with dj’s be the discretization points.