# A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering

arXiv: https://arxiv.org/abs/1701.09177 · HTML: https://mlsanity.com/paper/1701.09177/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2017.

## Built on by (most cited first, 16 of 16)

- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Mitigating Performance Saturation in Neural Marked Point Processes: Architectures and Loss Functions](https://mlsanity.com/paper/2107.03354/) (2021)
- [Multimodal Banking Dataset: Understanding Client Needs through Event Sequences](https://mlsanity.com/paper/2409.17587/) (2024)
- [Modeling Events and Interactions through Temporal Processes -- A Survey](https://mlsanity.com/paper/2303.06067/) (2023)
- [Powered Hawkes-Dirichlet Process: Challenging Textual Clustering using a Flexible Temporal Prior](https://mlsanity.com/paper/2109.07170/) (2021)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Online Learning for Mixture of Multivariate Hawkes Processes](https://mlsanity.com/paper/2208.07961/) (2022)
- [What Drives Online Popularity: Author, Content or Sharers? Estimating Spread Dynamics with Bayesian Mixture Hawkes](https://mlsanity.com/paper/2406.03390/) (2024)
- [Row-clustering of a Point Process-valued Matrix](https://mlsanity.com/paper/2110.01207/) (2021)
- [DIVA: A Dirichlet Process Mixtures Based Incremental Deep Clustering Algorithm via Variational Auto-Encoder](https://mlsanity.com/paper/2305.14067/) (2023)
- [Unmixing Noise from Hawkes Process to Model Learned Physiological Events](https://mlsanity.com/paper/2406.16938/) (2024)
- [A Bayesian Mixture Model of Temporal Point Processes with Determinantal Point Process Prior](https://mlsanity.com/paper/2411.04397/) (2024)
- [Hawkes Processes on Graphons](https://mlsanity.com/paper/2102.02741/) (2021)
- [Continuous-time convolutions model of event sequences](https://mlsanity.com/paper/2302.06247/) (2023)
- [Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes](https://mlsanity.com/paper/2305.18412/) (2023)
- [Learning under Commission and Omission Event Outliers](https://mlsanity.com/paper/2501.13599/) (2025)

## Abstract (arXiv)

We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to a cluster is generated via the same Hawkes process with specific parameters, and different clusters correspond to different Hawkes processes. The prior distribution of the Hawkes processes is controlled via a Dirichlet distribution. We learn the model via a maximum likelihood estimator (MLE) and propose an effective variational Bayesian inference algorithm. We specifically analyze the resulting EM-type algorithm in the context of inner-outer iterations and discuss several inner iteration allocation strategies. The identifiability of our model, the convergence of our learning method, and its sample complexity are analyzed in both theoretical and empirical ways, which demonstrate the superiority of our method to other competitors. The proposed method learns the number of clusters automatically and is robust to model misspecification. Experiments on both synthetic and real-world data show that our method can learn diverse triggering patterns hidden in asynchronous event sequences and achieve encouraging performance on clustering purity and consistency.