Abstract This paper introduces Ordinal Generalized Matrix Learning Vector Quantization (ORGMLVQ), an enhanced version of the GMLVQ algorithm designed for classifying data with an inherent order among classes. ORGMLVQ incorporates ordinal constraints directly into the metric learning process, allowing the model to better capture the progression between categories-an important aspect in applications such as medical diagnostics or risk grading. Through experiments on multiple ordinal regression datasets, as well as standard UCI benchmarks and real-world problems, the proposed method demonstrates significant improvement of MAUC while maintaining the interpretability and prototype-based nature of the original GMLVQ. These results suggest that our method is a strong, interpretable alternative for learning from structured, ordered data.

Class imbalance problem is quite pervasive in our nowadays human practice. This problem basically refers to the skewness in the data underlying distribution which, in turn, imposes many difficulties on typical machine learning algorithms. To deal with the emerging issues arising from multi-class skewed distributions, existing efforts are mainly divided into two categories: model-oriented solutions and data-oriented techniques. Focusing on the latter, this paper presents a new over-sampling technique which is inspired by Mahalanobis distance. The presented over-sampling technique, called MDO (Mahalanobis Distance-based Over-sampling technique), generates synthetic samples which have the same Mahalanobis distance from the considered class mean as other minority class examples. By preserving the covariance structure of the minority class instances and intelligently generating synthetic samples along the probability contours, new minority class instances are modelled better for learning algorithms. Moreover, MDO can reduce the risk of overlapping between different class regions which are considered as a serious challenge in multi-class problems. Our theoretical analyses and empirical observations across wide spectrum multi-class imbalanced benchmarks indicate that MDO is the method of choice by offering statistical superior MAUC and precision compared to the popular over-sampling techniques.