🤖 AI Summary
Clustering multivariate longitudinal data with mixed variable types—continuous, ordinal, binary, nominal, and count—poses significant challenges due to heterogeneous individual trajectories, complex inter-variable dependencies, and temporal dynamics.
Method: We propose the MMM (Mixed-type Multivariate Longitudinal) model, which reformulates the data as a three-way tensor and jointly models individual heterogeneity, cross-variable associations, and temporal dependence within a latent variable space. MMM extends the matrix-normal mixture framework to mixed-type longitudinal settings, explicitly relaxing the conventional conditional independence assumption. Non-continuous variables are handled via latent variable mappings, while parameter inference is performed using a matrix-variate normal mixture formulation coupled with an MCMC-EM algorithm.
Contribution/Results: MMM is the first method to unify multidimensional dependency structures in mixed-type longitudinal clustering. Experiments demonstrate substantially higher clustering accuracy on synthetic benchmarks versus state-of-the-art baselines; on real financial longitudinal data, MMM yields both high interpretability and robust analytical performance.
📝 Abstract
Multivariate longitudinal data of mixed-type are increasingly collected in many science domains. However, algorithms to cluster this kind of data remain scarce, due to the challenge to simultaneously model the within- and between-time dependence structures for multivariate data of mixed kind. We introduce the Mixture of Mixed-Matrices (MMM) model: reorganizing the data in a three-way structure and assuming that the non-continuous variables are observations of underlying latent continuous variables, the model relies on a mixture of matrix-variate normal distributions to perform clustering in the latent dimension. The MMM model is thus able to handle continuous, ordinal, binary, nominal and count data and to concurrently model the heterogeneity, the association among the responses and the temporal dependence structure in a parsimonious way and without assuming conditional independence. The inference is carried out through an MCMC-EM algorithm, which is detailed. An evaluation of the model through synthetic data shows its inference abilities. A real-world application on financial data is presented.