Clustering Time Series with Nonlinear Dynamics: A Bayesian Non-Parametric and Particle-Based Approach
This addresses the challenge of identifying neural subgroups in neuroscience, but it is incremental as it builds on existing clustering and Bayesian methods.
The authors tackled the problem of clustering time series with nonlinear dynamics into an unknown number of groups, using a Bayesian non-parametric framework and particle-based methods, and applied it to neural data from mice to identify subsets of neurons responding similarly to fear stimuli.
We propose a general statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups. Our motivation comes from neuroscience, where an important problem is to identify, within a large assembly of neurons, subsets that respond similarly to a stimulus or contingency. Upon modeling the multiple time series as the output of a Dirichlet process mixture of nonlinear state-space models, we derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling cluster assignments and sampling parameter values that form the basis of the clustering. The Metropolis step employs recent innovations in particle-based methods. We apply the framework to clustering time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear.