An online AUC formulation for binary classification

The area under the ROC curve (AUC) provides a good scalar measure of ranking performance without requiring a specific threshold for performance comparison among classifiers. AUC is useful for imprecise environments since it operates independently with respect to class distributions and misclassification costs. A direct optimization of this AUC criterion thus becomes a natural choice for binary classifier design. However, a direct formulation based on the AUC criterion would require a high computational cost due to the drastically increasing input pair features. In this paper, we propose an online learning algorithm to circumvent this computational problem for binary classification. Different from those conventional recursive formulations, the proposed formulation involves a pairwise cost function which pairs up a newly arrived data point with those of opposite class in stored data. Moreover, with incorporation of a sparse learning into the online formulation, the computational effort can be significantly reduced. Our empirical results on three different scales of public databases show promising potential in terms of classification AUC, accuracy, and computational efficiency.