A non-negative matrix factorization framework for identifying modular patterns in metagenomic profile data

Abstract

Metagenomic studies sequence DNA directly from environmental samples to explore the structure and function of complex microbial and viral communities. Individual, short pieces of sequenced DNA ("reads") are classified into (putative) taxonomic or metabolic groups which are analyzed for patterns across samples. Analysis of such read matrices is at the core of using metagenomic data to make inferences about ecosystem structure and function. Non-negative matrix factorization (NMF) is a numerical technique for approximating high-dimensional data points as positive linear combinations of positive components. It is thus well suited to interpretation of observed samples as combinations of different components. We develop, test and apply an NMF-based framework to analyze metagenomic read matrices. In particular, we introduce a method for choosing NMF degree in the presence of overlap, and apply spectral-reordering techniques to NMF-based similarity matrices to aid visualization. We show that our method can robustly identify the appropriate degree and disentangle overlapping contributions using synthetic data sets. We then examine and discuss the NMF decomposition of a metabolic profile matrix extracted from 39 publicly available metagenomic samples, and identify canonical sample types, including one associated with coral ecosystems, one associated with highly saline ecosystems and others. We also identify specific associations between pathways and canonical environments, and explore how alternative choices of decompositions facilitate analysis of read matrices at a finer scale.

Functional Biogeography of Ocean Microbes Revealed through Non-Negative Matrix Factorization

“…We applied a concordance method (see Materials and Methods and [26]) to compare possible decomposition ranks, and found that 5 is a suitable rank for the NMF decomposition of the GOS data (Figure 1 in Text S1). This means that the observed Pfam profile matrix () can be stably approximated using 5 functional profiles and associated site profiles.…”

“…We applied NMF on the whole Pfam profile and we selected Pfams based on the correlation between their spatial distribution and the site profile of each component (Figure 3a). We contend that this correlation-based approach is preferable to “specificity-” [26] or “projection-” [27], [28] based methods, because it avoids undue bias toward either rare or ubiquitous Pfams (see Materials and Methods and Figure 4 in Text S1). …”

Inferring Aggregated Functional Traits from Metagenomic Data Using Constrained Non-negative Matrix Factorization: Application to Fiber Degradation in the Human Gut Microbiota

“…Parameter selection procedures proposed in most applications of NMF to biological data are based upon stability of the weight matrix W over several initializations of the iterative algorithm used to solve the problem [12, 13, 15, 16], in particular regarding the clustering of samples. Since our use of NMF focuses on extracting reproducible biological mechanisms characterized by the trait matrix H , we are more interested in biological stability than numerical one.…”

“…As mentioned in the introduction, NMF techniques were previously used as a “soft” clustering tool to compare samples from various ecosystems, ranging from marine environment to human body ([15, 16], [17]). However, our work focused on different aspects of NMF.…”

“…In particular Jiang and co-authors used this approach as a “soft” clustering tool in different ecosystems. They studied pathway abundances in diverse environmental ecosystems [15], compared habitats in marine ecosystems using protein families profiles [16] and human body sites using phylogenetic and functional data [17]. …”