Bayesian Nonparametric Dynamical Clustering of Time Series

2025-10-08

AI Summary

This paper addresses the challenges in dynamic time-series clustering—namely, unknown cluster count, frequent switching among linear dynamic regimes, and resultant redundant cluster splits. We propose a Bayesian nonparametric switching linear dynamical system (SLDS) model. Methodologically, we integrate the hierarchical Dirichlet process (HDP) with Gaussian process priors to jointly achieve unbounded cluster number estimation, adaptive regime switching, and unified modeling of intra-cluster temporal alignment and amplitude variation. Variational inference enables both offline and online learning. Experiments on public electrocardiogram (ECG) datasets demonstrate that our approach significantly improves pattern discovery accuracy and robustness while effectively suppressing over-segmentation. It strikes a favorable balance between dynamic evolution modeling and scalable clustering.

Technology Category

• Machine Learning: Clustering
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet process as a prior on the parameters of a Switching Linear Dynamical System and a Gaussian process prior to model the statistical variations in amplitude and temporal alignment within each cluster. By modeling the evolution of time series patterns, the method avoids unnecessary proliferation of clusters in a principled manner. We perform inference by formulating a variational lower bound for off-line and on-line scenarios, enabling efficient learning through optimization. We illustrate the versatility and effectiveness of the approach through several case studies of electrocardiogram analysis using publicly available databases.

Problem

• Models evolution of unbounded time series clusters
• Switches among unknown regimes with linear dynamics
• Avoids unnecessary cluster proliferation through pattern evolution

Innovation

• Bayesian nonparametric clustering of time series
• Switching linear dynamical system with hierarchical priors
• Variational inference for offline and online learning