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This paper introduces a Bayesian nonparametric framework for clustering time series data by modeling regime switches within linear dynamical systems, addressing the challenge of managing an unbounded number of clusters without overfitting. The method leverages hierarchical Dirichlet processes and Gaussian process priors to capture statistical variations in amplitude and temporal alignment, with applications demonstrated on electrocardiogram analysis. It represents a significant advancement in unsupervised learning for sequential data, offering principled inference for both offline and online scenarios.
Bayesian Nonparametric Dynamical Clustering of Time Series
arXiv:2510.06919v2 Announce Type: replace-cross 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.
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.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Applications (stat.AP)
arXiv:2510.06919 [stat.ML]
(or arXiv:2510.06919v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2510.06919 Focus to learn more arXiv-issued DOI via DataCite
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