Previous approaches are either based on regularisation or on the gen- eration of virtual (transformed) examples. We develop a new frame- work for learning linear classifiers under known transformations based on semidefinite programming. We present a new learning algorithm-- the Semidefinite Programming Machine (SDPM)--which is able to find a maximum margin hyperplane when the training examples are polynomial trajectories instead of single points. The solution is found to be sparse in dual variables and allows to identify those points on the trajectory with minimal real-valued output as virtual support vec- tors. Extensions to segments of trajectories, to more than one trans- formation parameter, and to learning with kernels are discussed.