KNN-based maximum margin and minimum volume hyper-sphere machine for imbalanced data classification

Imbalanced data classification is often met in our real life. In this paper, a novel k-nearest neighbor (KNN)-based maximum margin and minimum volume hyper-sphere machine (KNN-M³VHM) is presented for the imbalanced data classification. The basic idea is to construct two hyper-spheres with different centres and radiuses. The first one contains majority examples and the second one covers minority examples. When constructing the first hyper-sphere, we remove some redundant majority samples using k-nearest neighbor (KNN)-based strategy to balance two classes of samples. Meanwhile, we maximize the margin between two hyper-spheres and minimize their volumes, which can result in two tight boundaries around each class. Similar to the twin hyper-sphere support vector machine (THSVM), KNN-M³VHM solves two related SVM-type problems and avoids the matrix inverse operation when solving the convex optimization problems. KNN-M³VHM considers not only the within-class information but also the between-class margin, then it achieves better performance in comparison with other state-of-the-art algorithms. Experimental results on twenty-five datasets validate the significant advantages of our proposed algorithm.