A Quadratic Surface Minimax Probability Machine for Imbalanced Classification

In this paper, a kernel-free minimax probability machine model for imbalanced classification is proposed. In this model, a quadratic surface is adopted directly for separating the data points into two classes. By using two symmetry constraints to define the two worst-case classification accuracy rates, the model of maximizing both the F-1 value of the minority class and the classification accuracy rate of all the data points is proposed. The proposed model corresponds to a fractional programming problem. Since the two worst-case classification accuracy rates are the symmetry, the proposed model can be further simplified. After this, the alternating descent algorithm is adopted for efficiently solving. The proposed method reduces the computational costs by both using the kernel-free technique and adopting the efficient algorithm. Some numerical tests on benchmark datasets are conducted to investigate the classification performance of the proposed method. The numerical results demonstrate that the proposed method performs better when compared with the other state-of-the-art methods, especially for classifying the imbalanced datasets. The better performance for the imbalanced classification is also demonstrated on a Wholesale customers dataset. This method can provide methodological support for the research in areas such as customer segmentation.