Scalable Nonlinear AUC Maximization Methods

Abstract

The area under the ROC curve (AUC) is a widely used measure for evaluating classification performance on heavily imbalanced data. The kernelized AUC maximization machines have established a superior generalization ability compared to linear AUC machines because of their capability in modeling the complex nonlinear structures underlying most real-world data. However, the high training complexity renders the kernelized AUC machines infeasible for large-scale data. In this paper, we present two nonlinear AUC maximization algorithms that optimize linear classifiers over a finite-dimensional feature space constructed via the k-means Nyström approximation. Our first algorithm maximizes the AUC metric by optimizing a pairwise squared hinge loss function using the truncated Newton method. However, the second-order batch AUC maximization method becomes expensive to optimize for extremely massive datasets. This motivates us to develop a first-order stochastic AUC maximization algorithm that incorporates a scheduled regularization update and scheduled averaging to accelerate the convergence of the classifier. Experiments on several benchmark datasets demonstrate that the proposed AUC classifiers are more efficient than kernelized AUC machines while they are able to surpass or at least match the AUC performance of the kernelized AUC machines. We also show experimentally that the proposed stochastic AUC classifier is able to reach the optimal solution, while the other state-of-the-art online and stochastic AUC maximization methods are prone to suboptimal convergence. Code related to this paper is available at: https://sites.google.com/view/majdikhalid/.