Approximating the Neyman-Pearson detector with 2C-SVMs. Application to radar detection

This paper presents a study about the possibility of implementing approximations to the Neyman-Pearson detector with C-Support Vector Machines and 2C-Support Vector Machines. It is based on obtaining the functions these learning machines approximate to after training to minimize the empirical risk, and on the possible implementation of the Neyman-Pearson detector with these approximated functions. The function approximated by a C-Support Vector Machine after perfect training is a binary function, with only two possible outputs. When the output of the C-Support Vector Machine is compared to a threshold, whose value is the intermediate between the possible outputs, an implementation of the Maximum-A-Posteriori classifier is obtained. On the other hand, the function approximated by a 2C-Support Vector Machine after perfect training is also a binary function, but this machine implements the Neyman-Pearson detector for a fixed probability of false alarm and probability of detection pair, that can be selected with the parameter γ which controls the costs of the error function. Some experiments about radar detection have been carried out, in order to confirm the theoretical results. The results of these experiments allow us to confirm that the 2C-Support Vector Machine can implement very good approximations to the Neyman-Pearson detector.