Bayesian Network Classifiers are popular approaches for classification problems where instances have to be assigned to one of several classes. However, in many domains, it is necessary to assign instances to multiple classes at the same time. This task has been normally addressed either by (i) transforming the problem into a single-class scenario by defining a new class variable with all of the possible combinations of classes or, (ii) by building an independent classifier for each class variable. Either way, the resulting models do not capture all the relations and dependencies between classes and features resulting into unprecise multidimensional classifiers. In this paper, we introduce a two-step method for learning Multidimensional Bayesian Network Classifiers (MBC) from data based on mutual information measures. The first step of the method learns an initial MBC structure which then, in the second step, is refined. Our approach is simple and keeps all the interactions and dependencies among classes and features. The method was tested on three benchmark multidimensional data-sets. Preliminary experimental results show how our method outperforms state-of-the-art methods used in multidimensional classification.
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