## 1 Introduction
There are several methods to deal with this problem. They can be organized in the following categories [5]:  
* Data resampling: oversampling or undersampling procedures to modify the training set by creating or eliminating instances in order to obtain a balanced distribution of the instances belonging to each class. * Algorithmic modification: this involves the modification of the learning algorithms to make them more suitable for processing imbalanced data. * Cost-sensitive learning: this takes into account the misclassification costs, so that the different types of errors are treated in a different way. Sampling strategies are the most widely used. Oversampling the examples of the minority class and under-sampling those belonging to the majority class are two common preprocessing methods applied to deal with imbalanced datasets, but they have some well-known weaknesses. Many works in the literature propose different ways to implement these methods, and there are also some comparative studies about the performance of different resampling strategies [6], as well as about the evaluation of oversampling versus undersampling. Despite the fact that some of the studies yield contradictory results [7], most authors agree on the shortcomings associated with these approaches. Removing potentially valuable data is the main drawback of undersampling the majority class, while oversampling the minority class can cause both overfitting problems and an increase in the computational cost of inducing the models [8]. On the other hand, classification models, as decision trees induced from the oversampled datasets, are usually very large and complex [9]. The other approaches that deal with the problem of imbalanced data, algorithmic modification and cost-sensitive learning, are less often employed owing to certain difficulties in their application. Adapting every algorithm to imbalanced data demands a great effort and sometimes provides poorer results than resampling techniques. In addition, cost-sensitive learning usually requires domain experts to provide values to fill in the cost matrix containing the penalties for the different types of misclassification [5], which is a difficult endeavor. Regarding classification algorithms, some works have proved that the ensemble approaches usually present the best behavior when working with imbalanced data. These algorithms are often used to induce more reliable classifiers, using either unsampled or resampled datasets as input [10; 11; 12]. This subject will be discussed in more detail in subsequent sections. The aim of the present study is to propose a way of building reliable predictive models from imbalanced datasets, minimizing the negative effects of sampling strategies. The validation is performed through an empirical study in which, besides classical metrics, other novel metrics designed for imbalanced data classification are also applied. The results prove that a suitable combination of ensemble classifiers and controlled undersampling yields better results than other recognized methods. The rest of the paper is organized as follows: Some important work in the literature about the topic under study is described in Section 2. Section 3 is devoted to introducing background information about the validation and classification approaches, as well as to presenting the proposed method. Specifically, the Section 3.1 presents the validation metrics used in imbalanced data contexts. The Section 3.2 includes the basis of the classification algorithms used in this work, with special emphasis on ensemble classifiers. The presentation and the rationale of the proposed approach are given in Section 3.3. The experimental study and its results are reported in Section 4, and the discussion of these results is to be found in Section 5. Finally, the conclusions are discussed in the last section.