Nonparametric Bayesian Multi-Facet Clustering for Longitudinal Data

Complex real-world time series data are inherently multi-faceted, e.g., temporal data can be described by seasonality and trend. Popular clustering methods typically aggregate information from all facets, treating them collectively rather than individually. This aggregation may diminish the interpretability of clusters by obscuring the specific contributions of individual facets to the clustering outcome. This limitation can be addressed by multi-facet clustering that builds a separate clustering model for each facet simultaneously. In this paper, we explore Bayesian multi-facet clustering modelling for temporal data using nonparametric priors to select an appropriate number of clusters automatically and using variational inference to efficiently explore the parameter space. We apply this framework to nonlinear growth models and vector autoregressive models and observe their performance through simulation studies. We apply these models to real-world time series data from the English Longitudinal Study of Ageing (ELSA), highlighting its utility in identifying meaningful and interpretable clusters. These findings underscore the potential of the framework for advancing the analysis of multi-faceted longitudinal data in diverse fields. Code is available at \href{https://github.com/Demi-wlw/Nonparametric-Bayesian-Multi-Facet-Clustering-for-Longitudinal-Data.git}{GitHub}.