Classification techniques and error control in logic mining

In this chapter we consider box clustering, a method for supervised classification that partitions the feature space with particularly simple convex sets (boxes). Box clustering produces systems of logic rules obtained from data in numerical form. Such rules explicitly represent the logic relations hidden in the data w.r.t. a target class. The algorithm adopted to solve the box clustering problem is based on a simple and fast agglomerative method which can be affected by the initial choice of the starting point and by the rules adopted by the method. In this chapter we propose and motivate a randomized approach that generates a large number of candidate models using different data samples and then chooses the best candidate model according to two criteria: model size, as expressed by the number of boxes of the model, and model precision, as expressed by the error on the test split. We adopt a Pareto-optimal strategy for the choice of the solution, under the hypothesis that such a choice would identify simple models with good predictive power. This procedure has been applied to a wide range of well-known data sets to evaluate to what extent our results confirm this hypothesis; its performances are then compared with those of competing methods.