A Nearest Neighbor Algorithm for Imbalanced Classification

Due to the inability of the accuracy-driven methods to address the challenging problem of learning from imbalanced data, several alternative measures have been proposed in the literature, like the Area Under the ROC Curve (AUC), the Average Precision (AP), the F-measure, the G-Mean, etc. However, these latter measures are neither smooth, convex nor separable, making their direct optimization hard in practice. In this paper, we tackle the challenging problem of imbalanced learning from a nearest-neighbor (NN) classification perspective, where the minority examples typically belong to the class of interest. Based on simple geometrical ideas, we introduce an algorithm that rescales the distance between a query sample and any positive training example. This leads to a modification of the Voronoi regions and thus of the decision boundaries of the NN classifier. We provide a theoretical justification about this scaling scheme which inherently aims at reducing the False Negative rate while controlling the number of False Positives. We further formally establish a link between the proposed method and cost-sensitive learning. An extensive experimental study is conducted on many public imbalanced datasets showing that our method is very effective with respect to popular Nearest-Neighbor algorithms, comparable to state-of-the-art sampling methods and even yields the best performance when combined with them.