We introduce a multi-type interacting particle system on graphs to model heterogeneous agent-based dynamics. Within this framework, we develop algorithms that jointly learn the interaction kernels, the latent type assignments, and the underlying graph structure. The approach has two stages: (i) a low-rank matrix sensing step that recovers a shared interaction embedding, and (ii) a clustering step that identifies the discrete types. Under the assumption of the restricted isometry property (RIP), we obtain theoretical guarantees on sample complexity and convergence for a wide range of model parameters.
