Abstract
The purpose of this paper is to introduce, for the first time, a distance metric learning algorithm for monotonic classification. Monotonic classification is performed on labeled data in which both input and output data have an order relation. It addresses the problem of predicting labels in such a way that, if the data to be predicted is greater or lower than any training sample, its prediction should be greater or lower as well. On a different note, the use of distance metric learning algorithms enables significant performance improvements in distance-based classifiers, such as the nearest neighbors classifier. Several distance-based classifiers that are able to respect the monotonicity constraints of the datasets have been proposed. However, the development of distance metric learning algorithms remains a challenge, since, when these algorithms transform the space they can negatively modify the monotonic constraints. In our work, we propose a new methodology for learning distances that does not corrupt these constraints and allows for the reduction of the nonmonotonicity of the dataset as well. The conducted experimental analysis also shows that the learned distances allow to improve the performance of the analyzed classifiers.