Open-set recognition (OSR) has achieved significant importance in recent years. For a robust recognition system, we need to identify the right class from a myriad of knowns and unknowns. In this work, we build and compare OSR systems for patient activity recognition (PAR) using compact radar sensors in a hospital setting. Radar sensors are an important part of a privacy-preserving monitoring system. Specifically, the proposed approach is based on a deep discriminative representation network (DDRN) trained using the large margin cosine loss (LMCL) and triplet loss (TL). A probability of an inclusion model in the embedding space based on the Weibull distribution is able to separate knowns from unknowns. This overall approach limits the risk of open space and enables us to easily identify any unknown activities. Our experiments show that the proposed approach is significantly better for open-set human activity recognition (HAR) with radar when compared with the state-of-the-art open-set approaches.