In recent years, there has been growing interest in leveraging machine learning for homeless service assignment. However, the categorical nature of administrative data recorded for homeless individuals hinders the development of accurate machine learning methods for this task. This work asserts that deriving latent representations of such features, while at the same time leveraging underlying relationships between instances is crucial in algorithmically enhancing the existing assignment decision-making process. Our proposed approach learns temporal and functional relationships between services from historical data, as well as unobserved but relevant relationships between individuals to generate features that significantly improve the prediction of the next service assignment compared to the state-of-the-art.