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In this paper we describe a new approach to dynamic signature verification using the discriminative training framework. The authentic and forgery samples are represented by two separate Gaussian Mixture models and discriminative training is used to achieve optimal separation between the two models. An enrollment sample clustering and screening procedure is described which improves the robustness of the system. We also introduce a method to estimate and apply subject norms representing the "typical" variation of the subject's signatures. The subject norm functions are parameterized, and the parameters are trained as an integral part of the discriminative training. The system was evaluated using 480 authentic signature samples and 260 skilled forgery samples from 44 accounts and achieved an equal error rate of 2.25%.