# MMM: Clustering Multivariate Longitudinal Mixed-type Data

arXiv: https://arxiv.org/abs/2509.12166 · HTML: https://mlsanity.com/paper/2509.12166/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 60 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Survey of state-of-the-art mixed data clustering algorithms](https://mlsanity.com/paper/1811.04364/) (2018)
- [Model Based Clustering for Mixed Data: clustMD](https://mlsanity.com/paper/1511.01720/) (2015)
- [High-dimensional Mixed Graphical Models](https://mlsanity.com/paper/1304.2810/) (2013)
- [Finite mixtures of matrix-variate Poisson-log normal distributions for three-way count data](https://mlsanity.com/paper/1807.08380/) (2018)
- [Model-based clustering of Gaussian copulas for mixed data](https://mlsanity.com/paper/1405.1299/) (2014)
- [A review of Monte Carlo-based versions of the EM algorithm](https://mlsanity.com/paper/2401.00945/) (2024)
- [Covariance pattern mixture models for the analysis of multivariate heterogeneous longitudinal data](https://mlsanity.com/paper/1401.1301/) (2014)
- [Copula Graphical Models for Heterogeneous Mixed Data](https://mlsanity.com/paper/2210.13140/) (2022)
- [Longitudinal Mixed Membership trajectory models for disability survey data](https://mlsanity.com/paper/1309.2324/) (2013)
- [Parsimonious Hidden Markov Models for Matrix-Variate Longitudinal Data](https://mlsanity.com/paper/2107.04330/) (2021)
- [Clustering Longitudinal Ordinal Data via Finite Mixture of Matrix-Variate Distributions](https://mlsanity.com/paper/2401.14827/) (2024)

## Abstract (arXiv)

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.