We study knowledge-based isocenter selection approaches in radiosurgery planning. In particular, we want to leverage recent advances in deep learning to predict isocenter locations in treatment plans in order to reduce costs and provide decision support. We begin by investigating desirable mathematical properties for the representation of treatment plans, which leads us to introduce the notion of tumor spaces. Our method can be summarized as follows: (1) compute and normalize tumor spaces, (2) compute shape descriptors for each tumor space and corresponding isocenters in order to reduce dimensionality, (3) train a residual neural-network on computed shape descriptors, and (4) predict isocenters for a given out-of-sample case using trained neural-network and (5) apply inverse transform to obtain result in voxel domain. Finally, our network was trained on 533 patient cases and was validated on the out-of-sample set of cases. Our numerical results indicate a positive predictive value of the proposed method.