  High-throughput sequencing technology provides unprecedented opportunities to
quantitatively explore human gut microbiome and its relation to diseases.
Microbiome data are compositional, sparse, noisy, and heterogeneous, which pose
serious challenges for statistical modeling. We propose an identifiable
Bayesian multinomial matrix factorization model to infer overlapping clusters
on both microbes and hosts. The proposed method represents the observed
over-dispersed zero-inflated count matrix as Dirichlet-multinomial mixtures on
which latent cluster structures are built hierarchically. Under the Bayesian
framework, the number of clusters is automatically determined and available
information from a taxonomic rank tree of microbes is naturally incorporated,
which greatly improves the interpretability of our findings. We demonstrate the
utility of the proposed approach by comparing to alternative methods in
simulations. An application to a human gut microbiome dataset involving
patients with inflammatory bowel disease reveals interesting clusters, which
contain bacteria families Bacteroidaceae, Bifidobacteriaceae,
Enterobacteriaceae, Fusobacteriaceae, Lachnospiraceae, Ruminococcaceae,
Pasteurellaceae, and Porphyromonadaceae that are known to be related to the
inflammatory bowel disease and its subtypes according to biological literature.
Our findings can help generate potential hypotheses for future investigation of
the heterogeneity of the human gut microbiome.
