Bayesian Nonparametric Dynamical Clustering of Time Series

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. Index T erms--Time series analysis, Bayesian methods, Gaussian processes, linear dynamical systems, Dirichlet processes, unsupervised learning, electrocardiogram, arrhythmia detection. IME series data analysis has come to pervade all scientific and technological domains, driven by the need to understand change over time. With the growing availability of such data, machine learning has assumed an increasingly central role in a wide variety of tasks which fall under the category of pattern recognition. Particularly, there is growing interest in identifying similar behaviors in time series data as a preliminary step towards generating insights into the dynamics of the underlying processes. Some recent methodologies can be found for characterizing sea wave conditions [1], transcriptome-wide gene expression profiling [2], selecting stocks with different share price performance [3], and discovering human motion primitives [4].