Chain based sampling for monotonic imbalanced classification

Classification with monotonic constraints arises from some ordinal real-life problems. In these real-life problems, it is common to find a big difference in the number of instances representing middle-ranked classes and the top classes, because the former usually represents the average or the normality, while the latter are the exceptional and uncommon. This is known as class imbalance problem, and it deteriorates the learning of those under-represented classes. However, the traditional solutions cannot be applied to applications that require monotonic restrictions to be asserted. Since these were not designed to consider monotonic constraints, they compromise the monotonicity of the data-sets and the performance of the monotonic classifiers. In this paper, we propose a set of new sampling techniques to mitigate the imbalanced class distribution and, at the same time, maintain the monotonicity of the data-sets. These methods perform the sampling inside monotonic chains, sets of comparable instances, in order to preserve them and, as a result, the monotonicity. Five different approaches are redesigned based on famous under- and over-sampling techniques and their standard and ordinal versions are compared with outstanding results.