Bayesian Nonparametric Joint Mixture Model for Clustering Spatially Correlated Time Series

Abstract

We develop a Bayesian nonparametric joint mixture model for clustering spatially correlated time series based on both spatial and temporal similarities. In the temporal perspective, the pattern of a time series is flexibly modeled as a mixture of Gaussian processes, with a Dirichlet process (DP) prior over mixture components. In the spatial perspective, the spatial location is incorporated as a feature for clustering, like a time series being incorporated as a feature. Namely, we model the spatial distribution of each cluster as a DP Gaussian mixture density. For the proposed model, the number of clusters does not need to be specified in advance, but rather is automatically determined during the clustering procedure. Moreover, the spatial distribution of each cluster can be flexibly modeled with multiple modes, without determining the number of modes or specifying spatial neighborhood structures in advance. Variational inference is employed for the efficient posterior computation of the proposed model. We validate the proposed model using simulated and real-data examples. Supplementary materials for the article are available online.

Keywords:

• Clustering
• Dirichlet process
• Gaussian process
• Mixture model
• Spatio-temporal data

Supplementary Materials

The codes and data for the simulated example can be downloaded online.

Acknowledgments

The authors thank the editor, associate editor, and referees for reviewing the article and providing valuable comments.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2018R1C1B6004511).