Automatic determination of reject thresholds in classifiers employing discriminant functions

In most statistical pattern classifiers, each class has different error probabilities. If a reject threshold is introduced, the error and reject probabilities can still vary widely for different classes. An algorithm is developed for finding separate reject thresholds for each class in order to attempt to equalize the probabilities. A gradient approach is used to minimize a measure of the difference between the desired and actual reject and error probabilities for each class. Examples are given for a Gaussian classifier of handprinted numerals. However, the method is applicable in any classifier employing discriminant functions. It is possible to significantly improve the tradeoff between error and reject probabilities, when the thresholds are allowed to be different for each class