Receiver Operating Characteristics of Perceptrons : In uence of Sample Size

In many practical classiication problems it is important to distinguish false positive from false negative results when evaluating the performance of the classiier. This is of particular importance for medical diagnostic tests. In this context, receiver operating characteristic (ROC) curves have become a standard tool. Here we apply this concept to characterize the performance of a simple neural network. Investigating the binary classiication of a perceptron we calculate analytically the shape of the corresponding ROC curves. The innuence of the size of the training set and the prevalence of the quality considered are studied by means of a statistical-mechanics analysis.