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A natural way of handling imbalanced data is to attempt to equalise the class frequencies and train the classifier of choice on balanced data. For two-class imbalanced problems, the classification success is typically measured by the geometric mean (GM) of the true positive and true negative rates. Here we prove that GM can be improved upon by instance selection, and give the theoretical conditions for such an improvement. We demonstrate that GM is non-monotonic with respect to the number of retained instances, which discourages systematic instance selection. We also show that balancing the distribution frequencies is inferior to a direct maximisation of GM. To verify our theoretical findings, we carried out an experimental study of 12 instance selection methods for imbalanced data, using 66 standard benchmark data sets. The results reveal possible room for new instance selection methods for imbalanced data.

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The theoretical background to automata and formal languages represents a complex learning area for students. Computer tools for interacting with the algorithm and interfaces to visualize its different steps can assist the learning process and make it more attractive. In this paper, we present a web application for learning some of the most common algorithms in an appealing way. They are specifically linked to the recognition of regular languages that are, taught in classes on both automata theory and compiler design. Although several simulators are available to students, they usually only serve to validate grammars, automata, and languages, rather than helping students to learn the internal processes that an algorithm can perform. The resource presented here can execute and display each algorithm process, step by step, providing explanations on each step that assist student comprehension. Additionally, as a web‐based resource, it can be used on any device with no need for specific software installation.

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Random Balance strategy (RandBal) has been recently proposed for constructing classifier ensembles for imbalanced, two-class data sets. In RandBal, each base classifier is trained with a sample of the data with a random class prevalence, independent of the a priori distribution. Hence, for each sample, one of the classes will be undersampled while the other will be oversampled. RandBal can be applied on its own or can be combined with any other ensemble method. One particularly successful variant is RandBalBoost which integrates Random Balance and boosting. Encouraged by the success of RandBal, this work proposes two approaches which extend RandBal to multiclass imbalance problems. Multiclass imbalance implies that at least two classes have substantially different proportion of instances. In the first approach proposed here, termed Multiple Random Balance (MultiRandBal), we deal with all classes simultaneously. The training data for each base classifier are sampled with random class proportions. The second approach we propose decomposes the multiclass problem into two-class problems using one-vs-one or one-vs-all, and builds an ensemble of RandBal ensembles. We call the two versions of the second approach OVO-RandBal and OVA-RandBal, respectively. These two approaches were chosen because they are the most straightforward extensions of RandBal for multiple classes. Our main objective is to evaluate both approaches for multiclass imbalanced problems. To this end, an experiment was carried out with 52 multiclass data sets. The results suggest that both MultiRandBal, and OVO/OVA-RandBal are viable extensions of the original twoclass RandBal. Collectively, they consistently outperform acclaimed state-of-the art methods for multiclass imbalanced problems.

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