Nested dirichlet hawkes process: a unified model for activity sequence-based user clustering

Activity sequence-based user clustering leverages complementary information about user behavior (e.g., life rhythms and action interests) to group users, providing a foundation for personalized services on online platforms. Existing methods typically model only life rhythms, which can lead to inaccurate clustering. In particular, users with similar life rhythms but different action interests, or vice versa, are often misgrouped. This limitation stems from the heterogeneous nature of user behavior, which makes it difficult to capture these two aspects simultaneously. Specifically, action interests are categorical (e.g., specific movie genres), while life rhythms are continuous and time-dependent (e.g., timing and frequency of actions). To address this limitation, we propose the Nested Dirichlet Hawkes Process (nDHP), a novel generative model that clusters users by modeling behavior patterns which jointly capture life rhythms and action interests via coupled semantic and temporal patterns. In nDHP, semantic patterns are captured by a multinomial distribution over actions, while temporal patterns are modeled by a Hawkes process over irregular activity timestamps. A nested Dirichlet process enables flexible clustering of users based on shared behavior patterns. For efficient inference, we develop a nested Sequential Monte Carlo (nSMC) algorithm tailored to the hierarchical structure of the model. Experiments on synthetic datasets validate the effectiveness of nDHP in discovering behavior patterns and demonstrate superior clustering accuracy compared to baselines. On real-world datasets, the model achieves more stable clustering, while visualizations of the learned behavior patterns demonstrate model interpretability.