Learning Microbial Community Structures with Supervised and Unsupervised Non-negative Matrix Factorization

Yun Cai, Hong Gu, Toby Kenney

Learning the structure of microbial communities is critical in understanding the different community structures and functions of microbes in distinct individuals. We view microbial communities as consisting of many subcommunities which are formed by certain groups of microbes functionally dependent on each other. The focus of this paper is on methods for extracting the subcommunities from the data, in particular Non-Negative Matrix Factorization (NMF). Our methods can be applied to both OTU data and functional metagenomic data. We apply the existing unsupervised NMF method and also develop a new supervised NMF method for extracting interpretable information from classification problems. The relevance of the subcommunities identified by NMF is demonstrated by their excellent performance for classification. Through three data examples, we demonstrate how to interpret the features identified by NMF to draw meaningful biological conclusions and discover hitherto unidentified patterns in the data. Comparing whole metagenomes of various mammals, (Muegge et al., Science 332:970-974, 2011), the biosynthesis of macrolides pathway is found in hindgut-fermenting herbivores, but not carnivores. This is consistent with results in veterinary science that macrolides should not be given to non-ruminant herbivores. For time series microbiome data from various body sites (Caporaso et al., Genome Biol 12:50, 2011), a shift in the microbial communities is identified for one individual. The shift occurs at around the same time in the tongue and gut microbiomes, indicating that the shift is a genuine biological trait, rather than an artefact of the method. For whole metagenome data from IBD patients and healthy controls (Qin et al., Nature 464:59-65, 2010), we identify differences in a number of pathways (some known, others new). NMF is a powerful tool for identifying the key features of microbial communities. These identified features can not only be used to perform difficult classification problems with a high degree of accuracy, they are also very interpretable and can lead to important biological insights into the structure of the communities. In addition, NMF is a dimension-reduction method (similar to PCA) in that it reduces the extremely complex microbial data into a low-dimensional representation, allowing a number of analyses to be performed more easily-for example, searching for temporal patterns in the microbiome. When we are interested in the differences between the structures of two groups of communities, supervised NMF provides a better way to do this, while retaining all the advantages of NMF-e.g. interpretability and a simple biological intuition.