On the difference between optimal combination functions for verification and identification systems

We have investigated different scenarios of combining pattern matchers. The combination problem can be viewed as a construction of a postprocessing classifier operating on the matching scores of the combined matchers. The optimal combination algorithm for verification systems corresponds to the likelihood ratio combination function. It can be implemented by the direct reconstruction of this function with genuine and impostor score density approximations. However, the optimal combination algorithm for identification systems is difficult to express analytically. We will show that this difficulty is caused by the dependencies between matching scores assigned to different classes by the same classifier. The experiments on the large sets of scores from handwritten word recognizers operating on postal images and biometric matchers (NIST biometric score set BSSR1) confirm the existence of such dependencies and that the optimal combination functions for verification and identification systems are different.