In order to return to a healthy daily life of individuals who need rehabilitation exercise, it is necessary to provide continuous individualized rehabilitation exercise services after discharge at the hospital. However, in reality, it is difficult to provide services for the entire rehabilitation cycle of individuals because hospital and community rehabilitation data are not shared. In this paper, we consider the problem of providing a top-k similar patient list under the assumption that rehabilitation medical care and community exercise service are shared. The considered problem differs from the typical recommender system problems due to the lack of labels representing any two patients share the same or similar characteristics, which means that it is challenging to apply the existing recommender algorithms. We present a mathematical programming-based approach that enables us to identify the optimal feature set and similarity between patients. Then, a two-step algorithm was developed by utilizing the presented mathematical formulation, which results in a user-based collaborative filtering system. We report the experimental results for 12 experimental options using real-life clinical data of low back pain patients.