Metric learning for monotonic classification: turning the space up to the limits of monotonicity

Abstract

This paper presents, for the first time, a distance metric learning algorithm for monotonic classification. Monotonic datasets arise in many real-world applications, where there exist order relations in the input and output variables, and the outputs corresponding to ordered pairs of inputs are also expected to be ordered. Monotonic classification can be addressed through several distance-based classifiers that are able to respect the monotonicity constraints of the data. The performance of distance-based classifiers can be improved with the use of distance metric learning algorithms, which are able to find the distances that best represent the similarities among each pair of data samples. However, learning a distance for monotonic data has an additional drawback: the learned distance may negatively impact the monotonic constraints of the data. In our work, we propose a new model for learning distances that does not corrupt these constraints. This methodology will also be useful in identifying and discarding non-monotonic pairs of samples that may be present in the data due to noise. The experimental analysis conducted, supported by a Bayesian statistical testing, demonstrates that the distances obtained by the proposed method can enhance the performance of several distance-based classifiers in monotonic problems.