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Discrete data such as counts of microbiome taxa resulting fromnext-generation sequencing are routinely encountered in bioinformatics. Taxacount data in microbiome studies are typically high-dimensional,over-dispersed, and can only reveal relative abundance therefore being treatedas compositional. Analyzing compositional data presents many challenges becausethey are restricted on a simplex. In a logistic normal multinomial model, therelative abundance is mapped from a simplex to a latent variable that exists onthe real Euclidean space using the additive log-ratio transformation. While alogistic normal multinomial approach brings in flexibility for modeling thedata, it comes with a heavy computational cost as the parameter estimationtypically relies on Bayesian techniques. In this paper, we develop a novelmixture of logistic normal multinomial models for clustering microbiome data.Additionally, we utilize an efficient framework for parameter estimation usingvariational Gaussian approximations (VGA). Adopting a variational Gaussianapproximation for the posterior of the latent variable reduces thecomputational overhead substantially. The proposed method is illustrated onsimulated and real datasets.

Clustering microbiome data using mixtures of logistic normal multinomial models