A research of optimal rejection thresholds based on ROC curve

A new method is proposed in this paper to determine the rejection thresholds. First, the minimum risk decision rules are analyzed and the cost function is founded. After taking into account the rejection cost, the cost function is modified and the requirement that the rejection thresholds shall satisfy to minimize the cost function is given. Second, the property of ROC is analyzed based on conditional probability density function, then the relationship between rejection thresholds and the tangent slope of any point is proved. Combining with the result of last step, the optimal rejection thresholds are determined. At last, experiments are carried out with four UCI datasets to prove the performance of the method proposed and the results show that this method not only can have a lower classification cost but also it is very stable in different datasets, which is significant for classification.