Supervised Density-Based Metric Learning Based on Bhattacharya Distance for Imbalanced Data Classification Problems

Learning distance metrics and distinguishing between samples from different classes are among the most important topics in machine learning. This article proposes a new distance metric learning approach tailored for highly imbalanced datasets. Imbalanced datasets suffer from a lack of data in the minority class, and the differences in class density strongly affect the efficiency of the classification algorithms. Therefore, the density of the classes is considered the main basis of learning the new distance metric. It is possible that the data of one class are composed of several densities, that is, the class is a combination of several normal distributions with different means and variances. In this paper, considering that classes may be multimodal, the distribution of each class is assumed in the form of a mixture of multivariate Gaussian densities. A density-based clustering algorithm is used for determining the number of components followed by the estimation of the parameters of the Gaussian components using maximum a posteriori density estimation. Then, the Bhattacharya distance between the Gaussian mixtures of the classes is maximized using an iterative scheme. To reach a large between-class margin, the distance between the external components is increased while decreasing the distance between the internal components. The proposed method is evaluated on 15 imbalanced datasets using the k-nearest neighbor (KNN) classifier. The results of the experiments show that using the proposed method significantly improves the efficiency of the classifier in imbalance classification problems. Also, when the imbalance ratio is very high and it is not possible to correctly identify minority class samples, the proposed method still provides acceptable performance.