Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process Mixture (1305.6659v2)

Abstract: This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM, and provides a hard clustering with convergence guarantees similar to those of the k-means algorithm. Empirical results from a synthetic test with moving Gaussian clusters and a test with real ADS-B aircraft trajectory data demonstrate that the algorithm requires orders of magnitude less computational time than contemporary probabilistic and hard clustering algorithms, while providing higher accuracy on the examined datasets.

• The paper introduces the Dynamic Means algorithm that uses low-variance asymptotic analysis of the DDPMM to achieve efficient hard clustering.
• The algorithm applies deterministic label and parameter updates, mirroring Kalman filter behavior for robust spatio-temporal data analysis.
• Empirical tests on synthetic and real-world streaming data reveal superior computational efficiency and accuracy over traditional methods.

Summary of Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process Mixture

The paper "Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process Mixture" presents an innovative algorithm tailored for clustering batch-sequential datasets characterized by an unknown and evolving number of clusters. This method stems from a low-variance asymptotic examination of the Gibbs sampling algorithm applied to the Dependent Dirichlet Process Mixture Model (DDPMM). It shares convergence properties with the k-means algorithm, producing hard clustering outcomes.

Core Contribution

The authors introduce the Dynamic Means algorithm, a novel clustering algorithm that leverages the dependent Dirichlet process mixture model to achieve hard clustering for spatio-temporal data. By examining the Gibbs sampling procedure asymptotically, they devise a deterministic alternative that circumvents the prohibitive computational demands typical of Bayesian nonparametric (BNP) inference methods, such as Gibbs sampling, particle learning, and variational inference.

Technical Approach

The DDPMM expands on the Dirichlet process mixture model by incorporating a mechanism for cluster evolution via birth, death, and transition processes. The technical novelty lies in the low-variance limit approach, which transforms the probabilistic inference process into deterministic label and parameter updates. By utilizing parameterization constants such as $\lambda$, $Q$, and $\tau$, these updates mimic traditional Kalman filter behavior in estimating dynamic changes in cluster means.

The algorithm's guarantee of convergence is substantiated through a cost function that decreases iteratively with each assignment of labels and updates of parameters. This approach integrates the flexibility inherent to BNP models with the computational efficiency of classical algorithms.

Empirical Evaluation

The efficacy of the Dynamic Means algorithm is demonstrated through synthetic data experiments involving moving Gaussian clusters and real-world applications on ADS-B aircraft trajectory data. Experimental results indicate superior computational efficiency and accuracy over state-of-the-art clustering algorithms. Notably, the algorithm showcases robustness to parameter variability and excels in situations requiring rapid inference on streaming data.

Implications and Future Work

The implications of this work span several domains where real-time data clustering is crucial, including autonomous robotic systems and real-time analytics in streaming environments. The algorithm's scalability and adaptability make it a powerful tool for clustering dynamically evolving datasets without pre-specified cluster counts.

For continued research, exploration into extending the algorithm's applicability to more complex data structures and hybrid models could be beneficial. Additionally, integrating this approach with other real-time decision-making systems could enhance the automation of adaptive processes in dynamic environments.

In summary, this paper contributes significantly to the clustering algorithm repertoire by bridging the gap between Bayesian nonparametric models and classical clustering efficiency, setting a foundation for further advancement in real-time data analysis and autonomous systems.