Abstract

Compositional distributions are very widely used in metagenomic/microbiome studies. Metagenomic/microbiome studies are used to identify and quantify the abundance of microbes in various environments such as soil (i.e., soil microbiome), oceans/seas (i.e., marine microbiome), plant tissues (i.e., endophytic microbiome), human body (i.e., human microbiome), etc. Clustering microbiome data can uncover meaningful patterns across samples, offering insights into biological variability and mechanisms. Microbiome data are typically high-dimensional, over-dispersed, and compositional, which complicates modelling. We propose a model-based clustering framework for longitudinal microbiome data using a mixture of logistic matrix-normal multinomial distributions, which jointly accounts for compositional structure and temporal dependence. Although this distribution provides greater flexibility in capturing complex correlations, it is computationally intensive. To overcome these limitations, we have developed a computationally efficient framework for parameter estimation using variational Gaussian approximations. The proposed approach is illustrated using both simulated and real datasets.